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114c0 00 48 8b 0d 60 6b 09 00 ff 15 7a d4 03 00 48 8b 15 33 66 09 00 45 33 c0 48 8b 0d 81 6e 09 00 e8 .H..`k....z...H..3f..E3.H...n...
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11540 58 a6 00 00 e9 42 03 00 00 48 8b 0d 58 63 09 00 48 89 05 51 63 09 00 48 29 19 75 06 ff 15 a6 d4 X....B...H..Xc..H..Qc..H).u.....
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11660 00 ff 15 19 d5 03 00 48 89 05 32 6b 09 00 ff 15 0c d5 03 00 48 89 05 2d 6b 09 00 ff 15 ff d4 03 .......H..2k........H..-k.......
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11700 f8 48 85 c0 75 16 48 8b 35 5b 58 04 00 bb 25 02 00 00 bd aa a6 00 00 e9 6f 01 00 00 48 8b 0d 95 .H..u.H.5[X...%.........o...H...
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11b40 48 8b ce ff 15 cf cf 03 00 48 83 2b 01 44 8b f0 75 09 48 8b cb ff 15 ad ce 03 00 45 85 f6 0f 88 H........H.+.D..u.H........E....
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11cc0 f8 ff 75 17 33 c0 48 89 0d 3b a7 08 00 48 83 f9 ff 0f 95 c0 ff c8 48 83 c4 28 c3 48 3b c1 74 21 ..u.3.H..;...H........H..(.H;.t!
11ce0 48 8b 0d 21 cc 03 00 48 8d 15 52 0b 09 00 48 8b 09 ff 15 d9 cd 03 00 b8 ff ff ff ff 48 83 c4 28 H..!...H..R...H.............H..(
11d00 c3 33 c0 48 83 c4 28 c3 cc cc cc cc cc cc cc cc 48 8d 0d 69 b5 08 00 48 ff 25 4a cb 03 00 cc cc .3.H..(.........H..i...H.%J.....
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11d80 48 8b c8 ff 15 c7 ca 03 00 48 8b d8 48 85 c0 75 2c 48 8b cf ff 15 d6 cd 03 00 4c 8d 0d 37 15 09 H........H..H..u,H........L..7..
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11e00 5c 24 28 4c 8b c0 48 89 6c 24 20 48 8b 09 ff 15 6c cc 03 00 eb 15 48 8b d5 ff 15 b1 cb 03 00 48 \$(L..H.l$.H....l.....H........H
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11e40 48 8b cf ff 15 bf cb 03 00 b8 ff ff ff ff 48 8b 5c 24 40 48 8b 6c 24 48 48 8b 74 24 50 48 83 c4 H.............H.\$@H.l$HH.t$PH..
11e60 30 5f c3 48 83 2e 01 75 09 48 8b ce ff 15 96 cb 03 00 48 8d 15 17 fa 08 00 48 8b cf ff 15 06 c9 0_.H...u.H........H......H......
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11ea0 75 15 48 8b cf ff 15 c5 cc 03 00 4c 8d 0d a6 13 09 00 e9 ea fe ff ff 48 8d 2d e2 14 09 00 48 8b u.H........L...........H.-....H.
11ec0 cb 48 8b d5 ff 15 be cd 03 00 48 8b cb 85 c0 75 1e ff 15 01 c9 03 00 48 8b cf 48 8b d8 ff 15 8d .H........H....u.......H..H.....
11ee0 cc 03 00 4c 8d 0d 6e 13 09 00 e9 01 ff ff ff 48 8b d5 ff 15 d8 ca 03 00 48 89 05 f1 5b 09 00 48 ...L..n........H........H...[..H
11f00 85 c0 0f 84 23 ff ff ff 48 83 2e 01 75 09 48 8b ce ff 15 f1 ca 03 00 4c 8d 0d f2 13 09 00 48 8b ....#...H...u.H........L......H.
11f20 cf 4c 8d 05 d8 57 09 00 48 8d 15 99 12 09 00 e8 3c 6c ff ff 85 c0 0f 88 fe fe ff ff 4c 8d 0d 3d .L...W..H.......<l..........L..=
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11f60 ff 4c 8d 0d 98 12 09 00 48 8b cf 4c 8d 05 66 61 09 00 48 8d 15 cf 11 09 00 e8 f2 6b ff ff 85 c0 .L......H..L..fa..H........k....
11f80 0f 88 b4 fe ff ff 4c 8d 0d e3 11 09 00 48 8b cf 4c 8d 05 19 5b 09 00 48 8d 15 3a 11 09 00 e8 cd ......L......H..L...[..H..:.....
11fa0 6b ff ff 85 c0 0f 88 8f fe ff ff 4c 8d 0d 3e 11 09 00 48 8b cf 4c 8d 05 0c 63 09 00 48 8d 15 a5 k..........L..>...H..L...c..H...
11fc0 10 09 00 e8 a8 6b ff ff 85 c0 0f 88 6a fe ff ff 4c 8d 0d a9 10 09 00 48 8b cf 4c 8d 05 47 5c 09 .....k......j...L......H..L..G\.
11fe0 00 48 8d 15 10 10 09 00 e8 83 6b ff ff 85 c0 0f 88 45 fe ff ff 4c 8d 0d 14 10 09 00 48 8b cf 4c .H........k......E...L......H..L
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12020 48 8b cf ff 15 df c9 03 00 48 8d 0d a0 0f 09 00 ff 15 0a cc 03 00 48 8b f8 48 85 c0 0f 84 07 fe H........H............H..H......
12040 ff ff 4c 8d 0d 37 0f 09 00 48 8b c8 4c 8d 05 25 58 09 00 48 8d 15 0e 0f 09 00 e8 11 6b ff ff 85 ..L..7...H..L..%X..H........k...
12060 c0 0f 88 d3 fd ff ff 4c 8d 0d a2 0e 09 00 48 8b cf 4c 8d 05 50 57 09 00 48 8d 15 79 0e 09 00 e8 .......L......H..L..PW..H..y....
12080 ec 6a ff ff 85 c0 0f 88 ae fd ff ff 4c 8d 0d 45 0e 09 00 48 8b cf 4c 8d 05 fb 57 09 00 48 8d 15 .j..........L..E...H..L...W..H..
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120c0 09 00 48 8d 15 9f 0d 09 00 e8 a2 6a ff ff 85 c0 0f 88 64 fd ff ff 4c 8d 0d 43 0d 09 00 48 8b cf ..H........j......d...L..C...H..
120e0 4c 8d 05 91 5e 09 00 48 8d 15 22 0d 09 00 e8 7d 6a ff ff 85 c0 0f 88 3f fd ff ff 4c 8d 0d e6 0c L...^..H.."....}j......?...L....
12100 09 00 48 8b cf 4c 8d 05 fc 5c 09 00 48 8d 15 bd 0c 09 00 e8 58 6a ff ff 85 c0 0f 88 1a fd ff ff ..H..L...\..H.......Xj..........
12120 4c 8d 0d 89 0b 09 00 48 8b cf 4c 8d 05 4f 60 09 00 48 8d 15 70 0b 09 00 e8 33 6a ff ff 85 c0 0f L......H..L..O`..H..p....3j.....
12140 88 f5 fc ff ff 4c 8d 0d 44 0a 09 00 48 8b cf 4c 8d 05 7a 59 09 00 48 8d 15 77 08 09 00 e8 0e 6a .....L..D...H..L..zY..H..w.....j
12160 ff ff 85 c0 0f 88 d0 fc ff ff 4c 8d 0d 8f 09 09 00 48 8b cf 4c 8d 05 6d 5f 09 00 48 8d 15 ca fa ..........L......H..L..m_..H....
12180 08 00 e8 e9 69 ff ff 85 c0 0f 88 ab fc ff ff 4c 8d 0d 4a 08 09 00 48 8b cf 4c 8d 05 38 55 09 00 ....i..........L..J...H..L..8U..
121a0 48 8d 15 19 08 09 00 e8 c4 69 ff ff 85 c0 0f 88 86 fc ff ff 4c 8d 0d e5 06 09 00 48 8b cf 4c 8d H........i..........L......H..L.
121c0 05 eb 60 09 00 48 8d 15 5c 06 09 00 e8 9f 69 ff ff 85 c0 0f 88 61 fc ff ff 48 83 2f 01 75 09 48 ..`..H..\.....i......a...H./.u.H
121e0 8b cf ff 15 20 c8 03 00 33 c0 e9 5f fc ff ff cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc ........3.._....................
12200 48 89 5c 24 08 48 89 6c 24 10 48 89 74 24 18 57 48 83 ec 30 48 8d 0d dd 10 09 00 ff 15 1f ca 03 H.\$.H.l$.H.t$.WH..0H...........
12220 00 48 8b f8 48 85 c0 0f 84 ec 00 00 00 48 8d 15 bc f6 08 00 48 8b c8 ff 15 4b c5 03 00 48 8b f0 .H..H........H......H....K...H..
12240 48 85 c0 0f 84 c1 00 00 00 48 8d 15 98 10 09 00 48 8b c8 ff 15 f7 c5 03 00 48 8b d8 48 85 c0 75 H........H......H........H..H..u
12260 2c 48 8b cf ff 15 06 c9 03 00 4c 8d 0d 77 10 09 00 48 8b 0d 90 c6 03 00 48 8d 15 09 a4 08 00 4c ,H........L..w...H......H......L
12280 8b c0 48 8b 09 ff 15 f5 c7 03 00 eb 6e 48 8d 2d a8 fb 08 00 48 8b cb 48 8b d5 ff 15 e8 c9 03 00 ..H.........nH.-....H..H........
122a0 48 8b cb 85 c0 75 3f ff 15 2b c5 03 00 48 8b cf 48 8b d8 ff 15 b7 c8 03 00 4c 8d 0d 28 10 09 00 H....u?..+...H..H........L..(...
122c0 48 8b 0d e1 c5 03 00 48 8d 15 d2 f5 08 00 48 89 5c 24 28 4c 8b c0 48 89 6c 24 20 48 8b 09 ff 15 H......H......H.\$(L..H.l$.H....
122e0 9c c7 03 00 eb 15 48 8b d5 ff 15 e1 c6 03 00 48 89 05 5a 55 09 00 48 85 c0 75 38 48 83 2e 01 75 ......H........H..ZU..H..u8H...u
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12320 5c 24 40 48 8b 6c 24 48 48 8b 74 24 50 48 83 c4 30 5f c3 48 83 2e 01 75 09 48 8b ce ff 15 c6 c6 \$@H.l$HH.t$PH..0_.H...u.H......
12340 03 00 48 8d 15 a7 f5 08 00 48 8b cf ff 15 36 c4 03 00 48 8b f0 48 85 c0 74 b0 48 8d 15 07 0f 09 ..H......H....6...H..H..t.H.....
12360 00 48 8b c8 ff 15 e6 c4 03 00 48 8b d8 48 85 c0 75 15 48 8b cf ff 15 f5 c7 03 00 4c 8d 0d e6 0e .H........H..H..u.H........L....
12380 09 00 e9 ea fe ff ff 48 8d 2d f6 f9 08 00 48 8b cb 48 8b d5 ff 15 ee c8 03 00 48 8b cb 85 c0 75 .......H.-....H..H........H....u
123a0 1e ff 15 31 c4 03 00 48 8b cf 48 8b d8 ff 15 bd c7 03 00 4c 8d 0d ae 0e 09 00 e9 01 ff ff ff 48 ...1...H..H........L...........H
123c0 8b d5 ff 15 08 c6 03 00 48 89 05 41 58 09 00 48 85 c0 0f 84 23 ff ff ff 48 83 2e 01 75 09 48 8b ........H..AX..H....#...H...u.H.
123e0 ce ff 15 21 c6 03 00 4c 8d 0d aa 10 09 00 48 8b cf 4c 8d 05 a8 51 09 00 48 8d 15 f9 0d 09 00 e8 ...!...L......H..L...Q..H.......
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12420 ff ff cc cc cc cc cc cc cc cc cc cc cc cc cc cc 48 89 5c 24 10 48 89 74 24 18 57 48 81 ec 20 01 ................H.\$.H.t$.WH....
12440 00 00 48 8b 05 17 90 06 00 48 33 c4 48 89 84 24 10 01 00 00 48 8d 0d dd 11 09 00 ff 15 df c7 03 ..H......H3.H..$....H...........
12460 00 48 8b d8 48 85 c0 0f 84 a3 08 00 00 48 89 ac 24 30 01 00 00 48 8b c8 48 8d 2d ad 11 09 00 48 .H..H........H..$0...H..H.-....H
12480 8b d5 ff 15 00 c3 03 00 33 f6 48 8b f8 48 85 c0 0f 84 c5 00 00 00 48 8b 48 08 39 b1 a8 00 00 00 ........3.H..H........H.H.9.....
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124e0 09 00 48 89 44 24 28 48 8d 15 32 fb 08 00 4c 8b cd 48 c7 44 24 20 70 03 00 00 48 8b 09 ff 15 7d ..H.D$(H..2...L..H.D$.p...H....}
12500 c5 03 00 eb 47 76 57 48 89 44 24 30 4c 8d 0d 0d 11 09 00 48 c7 44 24 28 70 03 00 00 4c 8d 05 8d ....GvWH.D$0L......H.D$(p...L...
12520 fa 08 00 ba c8 00 00 00 48 89 6c 24 20 48 8d 4c 24 40 ff 15 98 c7 03 00 45 33 c0 48 8d 54 24 40 ........H.l$.H.L$@......E3.H.T$@
12540 33 c9 ff 15 48 c7 03 00 85 c0 79 12 48 83 2f 01 75 09 48 8b cf ff 15 ad c4 03 00 48 8b fe 48 8b 3...H.....y.H./.u.H........H..H.
12560 ac 24 30 01 00 00 48 89 3d 63 5e 09 00 48 85 ff 0f 84 8b 07 00 00 48 83 2b 01 75 09 48 8b cb ff .$0...H.=c^..H........H.+.u.H...
12580 15 83 c4 03 00 48 8d 0d 84 10 09 00 ff 15 ae c6 03 00 48 8b d8 48 85 c0 0f 84 72 07 00 00 41 b9 .....H............H..H....r...A.
125a0 20 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 51 10 09 00 48 8b c8 48 8d 15 3b 10 09 00 e8 1e 9b .....D$.....L..Q...H..H..;......
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125e0 00 48 8d 0d 00 10 09 00 ff 15 52 c6 03 00 48 8b d8 48 85 c0 0f 84 16 07 00 00 41 b9 20 00 00 00 .H........R...H..H........A.....
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12620 05 7b 55 09 00 48 85 c0 0f 84 d3 06 00 00 48 83 2b 01 75 09 48 8b cb ff 15 cb c3 03 00 48 8d 0d .{U..H........H.+.u.H........H..
12640 80 0f 09 00 ff 15 f6 c5 03 00 48 8b d8 48 85 c0 0f 84 ba 06 00 00 48 8d 15 5f 0f 09 00 48 8b c8 ..........H..H........H.._...H..
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12680 00 4c 8d 0d 34 0f 09 00 4c 8d 05 25 0f 09 00 48 8d 15 d2 f4 08 00 48 8b 09 ff 15 e1 c3 03 00 eb .L..4...L..%...H......H.........
126a0 3d 48 8b 40 20 48 83 f8 60 73 45 48 8b 0d e6 c3 03 00 4c 8d 0d 03 0f 09 00 48 89 44 24 28 4c 8d =H.@.H..`sEH......L......H.D$(L.
126c0 05 ef 0e 09 00 48 8d 15 54 f9 08 00 48 c7 44 24 20 60 00 00 00 48 8b 09 ff 15 a2 c3 03 00 48 83 .....H..T...H.D$.`...H........H.
126e0 2f 01 75 09 48 8b cf ff 15 1b c3 03 00 48 8b fe 48 89 3d 99 53 09 00 48 85 ff 0f 84 01 06 00 00 /.u.H........H..H.=.S..H........
12700 48 8d 15 a1 0e 09 00 48 8b cb ff 15 78 c0 03 00 48 8b f8 48 85 c0 0f 84 81 00 00 00 48 8b 48 08 H......H....x...H..H........H.H.
12720 39 b1 a8 00 00 00 7c 27 48 8b 0d 79 c1 03 00 4c 8d 0d 72 0e 09 00 4c 8d 05 5f 0e 09 00 48 8d 15 9.....|'H..y...L..r...L.._...H..
12740 24 f4 08 00 48 8b 09 ff 15 33 c3 03 00 eb 3f 48 8b 40 20 48 3d 48 0a 00 00 73 45 48 8b 0d 36 c3 $...H....3....?H.@.H=H...sEH..6.
12760 03 00 4c 8d 0d 3f 0e 09 00 48 89 44 24 28 4c 8d 05 27 0e 09 00 48 8d 15 a4 f8 08 00 48 c7 44 24 ..L..?...H.D$(L..'...H......H.D$
12780 20 48 0a 00 00 48 8b 09 ff 15 f2 c2 03 00 48 83 2f 01 75 09 48 8b cf ff 15 6b c2 03 00 48 8b fe .H...H........H./.u.H....k...H..
127a0 48 89 3d f9 55 09 00 48 85 ff 0f 84 51 05 00 00 48 8d 15 d9 0d 09 00 48 8b cb ff 15 c8 bf 03 00 H.=.U..H....Q...H......H........
127c0 48 8b f8 48 85 c0 0f 84 81 00 00 00 48 8b 48 08 39 b1 a8 00 00 00 7c 27 48 8b 0d c9 c0 03 00 4c H..H........H.H.9.....|'H......L
127e0 8d 0d aa 0d 09 00 4c 8d 05 9b 0d 09 00 48 8d 15 74 f3 08 00 48 8b 09 ff 15 83 c2 03 00 eb 3f 48 ......L......H..t...H.........?H
12800 8b 40 20 48 3d 30 02 00 00 73 45 48 8b 0d 86 c2 03 00 4c 8d 0d 77 0d 09 00 48 89 44 24 28 4c 8d .@.H=0...sEH......L..w...H.D$(L.
12820 05 63 0d 09 00 48 8d 15 f4 f7 08 00 48 c7 44 24 20 30 02 00 00 48 8b 09 ff 15 42 c2 03 00 48 83 .c...H......H.D$.0...H....B...H.
12840 2f 01 75 09 48 8b cf ff 15 bb c1 03 00 48 8b fe 48 89 3d 39 56 09 00 48 85 ff 0f 84 a1 04 00 00 /.u.H........H..H.=9V..H........
12860 48 8d 15 19 0d 09 00 48 8b cb ff 15 18 bf 03 00 48 8b f8 48 85 c0 74 7f 48 8b 48 08 39 b1 a8 00 H......H........H..H..t.H.H.9...
12880 00 00 7c 27 48 8b 0d 1d c0 03 00 4c 8d 0d ee 0c 09 00 4c 8d 05 df 0c 09 00 48 8d 15 c8 f2 08 00 ..|'H......L......L......H......
128a0 48 8b 09 ff 15 d7 c1 03 00 eb 3d 48 8b 40 20 48 83 f8 60 73 45 48 8b 0d dc c1 03 00 4c 8d 0d bd H.........=H.@.H..`sEH......L...
128c0 0c 09 00 48 89 44 24 28 4c 8d 05 a9 0c 09 00 48 8d 15 4a f7 08 00 48 c7 44 24 20 60 00 00 00 48 ...H.D$(L......H..J...H.D$.`...H
128e0 8b 09 ff 15 98 c1 03 00 48 83 2f 01 75 09 48 8b cf ff 15 11 c1 03 00 48 8b fe 48 89 3d ef 59 09 ........H./.u.H........H..H.=.Y.
12900 00 48 85 ff 0f 84 f7 03 00 00 41 b9 10 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 51 0c 09 00 48 .H........A......D$.....L..Q...H
12920 8b cb 48 8d 15 3f 0c 09 00 e8 b2 97 ff ff 48 89 05 ab 4d 09 00 48 85 c0 0f 84 c3 03 00 00 41 b9 ..H..?........H...M..H........A.
12940 10 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 09 f5 08 00 48 8b cb 48 8d 15 03 0c 09 00 e8 7e 97 .....D$.....L......H..H.......~.
12960 ff ff 48 89 05 5f 4c 09 00 48 85 c0 0f 84 8f 03 00 00 41 b9 10 00 00 00 c7 44 24 20 01 00 00 00 ..H.._L..H........A......D$.....
12980 4c 8d 05 d1 0b 09 00 48 8b cb 48 8d 15 bf 0b 09 00 e8 4a 97 ff ff 48 89 05 fb 4b 09 00 48 85 c0 L......H..H.......J...H...K..H..
129a0 0f 84 5b 03 00 00 41 b9 10 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 85 0b 09 00 48 8b cb 48 8d ..[...A......D$.....L......H..H.
129c0 15 73 0b 09 00 e8 16 97 ff ff 48 89 05 9f 52 09 00 48 85 c0 0f 84 27 03 00 00 41 b9 10 00 00 00 .s........H...R..H....'...A.....
129e0 c7 44 24 20 01 00 00 00 4c 8d 05 39 0b 09 00 48 8b cb 48 8d 15 6b 07 09 00 e8 e2 96 ff ff 48 89 .D$.....L..9...H..H..k........H.
12a00 05 eb 54 09 00 48 85 c0 0f 84 f3 02 00 00 41 b9 10 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 15 ..T..H........A......D$.....L...
12a20 0a 09 00 48 8b cb 48 8d 15 b7 06 09 00 e8 ae 96 ff ff 48 89 05 77 4b 09 00 48 85 c0 0f 84 bf 02 ...H..H...........H..wK..H......
12a40 00 00 41 b9 10 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 c1 0a 09 00 48 8b cb 48 8d 15 13 06 09 ..A......D$.....L......H..H.....
12a60 00 e8 7a 96 ff ff 48 89 05 9b 4c 09 00 48 85 c0 0f 84 8b 02 00 00 41 b9 10 00 00 00 c7 44 24 20 ..z...H...L..H........A......D$.
12a80 01 00 00 00 4c 8d 05 9d 09 09 00 48 8b cb 48 8d 15 6f 05 09 00 e8 46 96 ff ff 48 89 05 17 50 09 ....L......H..H..o....F...H...P.
12aa0 00 48 85 c0 0f 84 57 02 00 00 41 b9 10 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 49 0a 09 00 48 .H....W...A......D$.....L..I...H
12ac0 8b cb 48 8d 15 ab 03 09 00 e8 12 96 ff ff 48 89 05 13 4d 09 00 48 85 c0 0f 84 23 02 00 00 41 b9 ..H...........H...M..H....#...A.
12ae0 10 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 05 0a 09 00 48 8b cb 48 8d 15 cf f3 08 00 e8 de 95 .....D$.....L......H..H.........
12b00 ff ff 48 89 05 17 4b 09 00 48 85 c0 0f 84 ef 01 00 00 48 8d 15 83 f3 08 00 48 8b cb ff 15 66 bc ..H...K..H........H......H....f.
12b20 03 00 48 8b f8 48 85 c0 0f 84 81 00 00 00 48 8b 48 08 39 b1 a8 00 00 00 7c 27 48 8b 0d 67 bd 03 ..H..H........H.H.9.....|'H..g..
12b40 00 4c 8d 0d 54 f3 08 00 4c 8d 05 05 f3 08 00 48 8d 15 12 f0 08 00 48 8b 09 ff 15 21 bf 03 00 eb .L..T...L......H......H....!....
12b60 3f 48 8b 40 20 48 3d e8 00 00 00 73 45 48 8b 0d 24 bf 03 00 4c 8d 0d 21 f3 08 00 48 89 44 24 28 ?H.@.H=....sEH..$...L..!...H.D$(
12b80 4c 8d 05 cd f2 08 00 48 8d 15 92 f4 08 00 48 c7 44 24 20 e8 00 00 00 48 8b 09 ff 15 e0 be 03 00 L......H......H.D$.....H........
12ba0 48 83 2f 01 75 09 48 8b cf ff 15 59 be 03 00 48 8b fe 48 89 3d 3f 58 09 00 48 85 ff 0f 84 3f 01 H./.u.H....Y...H..H.=?X..H....?.
12bc0 00 00 48 83 2b 01 75 09 48 8b cb ff 15 37 be 03 00 48 8d 0d 00 09 09 00 ff 15 62 c0 03 00 48 8b ..H.+.u.H....7...H........b...H.
12be0 d8 48 85 c0 0f 84 26 01 00 00 41 b9 60 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 c9 08 09 00 48 .H....&...A.`....D$.....L......H
12c00 8b c8 48 8d 15 9f 08 09 00 e8 d2 94 ff ff 48 89 05 63 49 09 00 48 85 c0 0f 84 e3 00 00 00 41 b9 ..H...........H..cI..H........A.
12c20 40 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 e5 07 09 00 48 8b cb 48 8d 15 bb 07 09 00 e8 9e 94 @....D$.....L......H..H.........
12c40 ff ff 48 89 05 4f 50 09 00 48 85 c0 0f 84 af 00 00 00 48 8b 15 57 3f 09 00 48 8b 88 08 01 00 00 ..H..OP..H........H..W?..H......
12c60 ff 15 f2 bb 03 00 48 8b f8 48 85 c0 74 44 33 d2 48 8b c8 ff 15 57 bd 03 00 48 8b f0 48 85 c0 75 ......H..H..tD3.H....W...H..H..u
12c80 22 ff 15 a1 bf 03 00 48 85 c0 75 17 48 8b 0d 55 bf 03 00 48 8d 15 7e eb 08 00 48 8b 09 ff 15 2d "......H..u.H..U...H..~...H....-
12ca0 be 03 00 48 83 2f 01 75 09 48 8b cf ff 15 56 bd 03 00 48 89 35 87 53 09 00 48 85 f6 74 43 41 b9 ...H./.u.H....V...H.5.S..H..tCA.
12cc0 10 00 00 00 c7 44 24 20 01 00 00 00 4c 8d 05 b5 06 09 00 48 8b cb 48 8d 15 8b 06 09 00 e8 fe 93 .....D$.....L......H..H.........
12ce0 ff ff 48 89 05 0f 53 09 00 48 85 c0 74 13 48 83 2b 01 75 09 48 8b cb ff 15 0b bd 03 00 33 c0 eb ..H...S..H..t.H.+.u.H........3..
12d00 14 48 83 2b 01 75 09 48 8b cb ff 15 f8 bc 03 00 b8 ff ff ff ff 48 8b 8c 24 10 01 00 00 48 33 cc .H.+.u.H.............H..$....H3.
12d20 e8 ab 4b ff ff 4c 8d 9c 24 20 01 00 00 49 8b 5b 18 49 8b 73 20 49 8b e3 5f c3 cc cc cc cc cc cc ..K..L..$....I.[.I.s.I.._.......
12d40 40 53 48 83 ec 20 48 8d 1d 23 a3 08 00 48 8b cb ff 15 2a ba 03 00 85 c0 0f 88 af 02 00 00 48 83 @SH...H..#...H....*...........H.
12d60 3d 2a a4 08 00 00 75 1d 48 8b 05 91 a3 08 00 48 3b 05 9a be 03 00 48 0f 44 05 92 be 03 00 48 89 =*....u.H......H;.....H.D.....H.
12d80 05 7b a3 08 00 48 8b 15 0c 3e 09 00 4c 8b c3 48 8b 0d 3a 54 09 00 ff 15 4c bf 03 00 85 c0 0f 88 .{...H...>..L..H..:T....L.......
12da0 69 02 00 00 48 8d 05 d5 47 09 00 48 89 1d a6 53 09 00 48 89 05 bf 4e 09 00 48 8d 1d e0 9e 08 00 i...H...G..H...S..H...N..H......
12dc0 48 8d 05 89 da 00 00 48 8b cb 48 89 05 af 47 09 00 ff 15 a9 b9 03 00 85 c0 0f 88 2e 02 00 00 48 H......H..H...G................H
12de0 8b 15 92 4e 09 00 48 8b 0d bb 9f 08 00 e8 ae 99 ff ff 85 c0 0f 88 13 02 00 00 48 8b cb e8 fe 93 ...N..H...................H.....
12e00 ff ff 85 c0 0f 88 03 02 00 00 48 89 1d 17 52 09 00 48 8d 1d 58 99 08 00 48 8b cb ff 15 5f b9 03 ..........H...R..H..X...H...._..
12e20 00 85 c0 0f 88 e4 01 00 00 48 83 3d 5f 9a 08 00 00 75 1d 48 8b 05 c6 99 08 00 48 3b 05 cf bd 03 .........H.=_....u.H......H;....
12e40 00 48 0f 44 05 c7 bd 03 00 48 89 05 b0 99 08 00 48 8b cb e8 a8 93 ff ff 85 c0 0f 88 ad 01 00 00 .H.D.....H......H...............
12e60 48 8d 05 d1 48 09 00 48 89 1d f2 54 09 00 48 89 05 83 52 09 00 48 8d 1d 44 a0 08 00 48 8d 05 1d H...H..H...T..H...R..H..D...H...
12e80 be 00 00 48 8b cb 48 89 05 ab 48 09 00 48 8d 05 5c b3 00 00 48 89 05 a5 48 09 00 48 8d 05 de af ...H..H...H..H..\...H...H..H....
12ea0 00 00 48 89 05 9f 48 09 00 48 8d 05 10 ac 00 00 48 89 05 99 48 09 00 48 8d 05 62 ab 00 00 48 89 ..H...H..H......H...H..H..b...H.
12ec0 05 93 48 09 00 48 8d 05 54 a4 00 00 48 89 05 8d 48 09 00 48 8d 05 e6 9d 00 00 48 89 05 87 48 09 ..H..H..T...H...H..H......H...H.
12ee0 00 ff 15 99 b8 03 00 85 c0 0f 88 1e 01 00 00 48 83 3d e9 a0 08 00 00 75 1d 48 8b 05 50 a0 08 00 ...............H.=.....u.H..P...
12f00 48 3b 05 09 bd 03 00 48 0f 44 05 01 bd 03 00 48 89 05 3a a0 08 00 48 8b 15 db 51 09 00 48 8b 0d H;.....H.D.....H..:...H...Q..H..
12f20 a4 a0 08 00 e8 77 98 ff ff 85 c0 0f 88 dc 00 00 00 48 8b cb e8 c7 92 ff ff 85 c0 0f 88 cc 00 00 .....w...........H..............
12f40 00 48 8d 05 10 4f 09 00 48 89 1d 69 4e 09 00 48 89 05 32 52 09 00 48 8b 05 9b 51 09 00 0f 10 00 .H...O..H..iN..H..2R..H...Q.....
12f60 0f 11 05 f1 4e 09 00 0f 10 48 10 0f 11 0d f6 4e 09 00 0f 10 40 20 48 8d 05 63 56 00 00 48 89 1d ....N....H.....N....@.H..cV..H..
12f80 fc 95 08 00 48 8d 1d f5 94 08 00 0f 11 05 e6 4e 09 00 48 89 05 e7 4e 09 00 48 8b cb 48 8d 05 bd ....H..........N..H...N..H..H...
12fa0 55 00 00 48 89 05 de 4e 09 00 ff 15 d0 b7 03 00 85 c0 78 59 48 83 3d e4 95 08 00 00 75 1d 48 8b U..H...N..........xYH.=.....u.H.
12fc0 05 4b 95 08 00 48 3b 05 44 bc 03 00 48 0f 44 05 3c bc 03 00 48 89 05 35 95 08 00 48 8b 15 a6 51 .K...H;.D...H.D.<...H..5...H...Q
12fe0 09 00 48 8b 0d 9f 95 08 00 e8 b2 97 ff ff 85 c0 78 1b 48 8b cb e8 06 92 ff ff 85 c0 78 0f 48 89 ..H.............x.H.........x.H.
13000 1d 63 53 09 00 33 c0 48 83 c4 20 5b c3 b8 ff ff ff ff 48 83 c4 20 5b c3 cc cc cc cc cc cc cc cc .cS..3.H...[......H...[.........
13020 33 c0 c3 cc cc cc cc cc cc cc cc cc cc cc cc cc 33 c0 c3 cc cc cc cc cc cc cc cc cc cc cc cc cc 3...............3...............
13040 48 8b 05 01 bb 03 00 48 89 05 2a 4b 09 00 48 ff 00 48 8b 05 f0 ba 03 00 48 89 05 49 48 09 00 48 H......H..*K..H..H......H..IH..H
13060 ff 00 48 8b 05 df ba 03 00 48 89 05 f8 49 09 00 48 ff 00 48 8b 05 ce ba 03 00 48 89 05 8f 4a 09 ..H......H...I..H..H......H...J.
13080 00 48 ff 00 48 8b 05 bd ba 03 00 48 89 05 ee 4b 09 00 48 ff 00 33 c0 c3 cc cc cc cc cc cc cc cc .H..H......H...K..H..3..........
130a0 40 53 48 83 ec 20 48 83 3d 92 a3 08 00 00 0f 84 8b 00 00 00 48 8d 1d 8d a3 08 00 0f 1f 44 00 00 @SH...H.=...........H........D..
130c0 0f b6 43 19 0a 43 18 48 8b 0b 74 31 80 7b 1a 00 74 08 ff 15 08 bc 03 00 eb 30 48 8b 53 08 4c 8b ..C..C.H..t1.{..t........0H.S.L.
130e0 43 10 48 ff ca 4d 85 c0 74 0b 45 33 c9 ff 15 bd b6 03 00 eb 15 ff 15 c5 b8 03 00 eb 0d 48 8b 53 C.H..M..t.E3.................H.S
13100 08 48 ff ca ff 15 76 b7 03 00 48 8b c8 48 8b 43 f8 48 89 08 48 8b 43 f8 48 8b 08 48 85 c9 0f 84 .H....v...H..H.C.H..H.C.H..H....
13120 b2 01 00 00 ff 15 96 ba 03 00 48 83 f8 ff 0f 84 a2 01 00 00 48 83 c3 28 48 83 7b f8 00 75 81 0f ..........H.........H..(H.{..u..
13140 57 c0 ff 15 a8 b9 03 00 48 89 05 81 4b 09 00 48 85 c0 0f 84 7e 01 00 00 f2 0f 10 05 c8 11 06 00 W.......H...K..H....~...........
13160 ff 15 8a b9 03 00 48 89 05 a3 4d 09 00 48 85 c0 0f 84 60 01 00 00 f2 0f 10 05 b2 11 06 00 ff 15 ......H...M..H....`.............
13180 6c b9 03 00 48 89 05 0d 49 09 00 48 85 c0 0f 84 42 01 00 00 f2 0f 10 05 84 11 06 00 ff 15 4e b9 l...H...I..H....B.............N.
131a0 03 00 48 89 05 27 47 09 00 48 85 c0 0f 84 24 01 00 00 f2 0f 10 05 86 11 06 00 ff 15 30 b9 03 00 ..H..'G..H....$.............0...
131c0 48 89 05 e1 51 09 00 48 85 c0 0f 84 06 01 00 00 33 c9 ff 15 f8 b9 03 00 48 89 05 d9 47 09 00 48 H...Q..H........3.......H...G..H
131e0 85 c0 0f 84 ee 00 00 00 b9 01 00 00 00 ff 15 dd b9 03 00 48 89 05 8e 4e 09 00 48 85 c0 0f 84 d3 ...................H...N..H.....
13200 00 00 00 b9 14 00 00 00 ff 15 c2 b9 03 00 48 89 05 d3 46 09 00 48 85 c0 0f 84 b8 00 00 00 b9 32 ..............H...F..H.........2
13220 00 00 00 ff 15 a7 b9 03 00 48 89 05 b0 49 09 00 48 85 c0 0f 84 9d 00 00 00 b9 95 99 ae 06 ff 15 .........H...I..H...............
13240 8c b9 03 00 48 89 05 e5 47 09 00 48 85 c0 0f 84 82 00 00 00 b9 37 35 2a 08 ff 15 71 b9 03 00 48 ....H...G..H.........75*...q...H
13260 89 05 2a 4b 09 00 48 85 c0 74 6b b9 31 89 06 0b ff 15 5a b9 03 00 48 89 05 d3 4d 09 00 48 85 c0 ..*K..H..tk.1.....Z...H...M..H..
13280 74 54 b9 00 ca 9a 3b ff 15 43 b9 03 00 48 89 05 5c 49 09 00 48 85 c0 74 3d 45 33 c0 48 8d 0d a5 tT....;..C...H..\I..H..t=E3.H...
132a0 03 09 00 33 d2 ff 15 85 b8 03 00 48 89 05 7e 4c 09 00 48 85 c0 74 1f b9 ff ff ff ff ff 15 0e b9 ...3.......H..~L..H..t..........
132c0 03 00 48 89 05 f7 48 09 00 48 85 c0 74 08 33 c0 48 83 c4 20 5b c3 b8 ff ff ff ff 48 83 c4 20 5b ..H...H..H..t.3.H...[......H...[
132e0 c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc 48 81 ec 88 00 00 00 48 8b 15 02 3b 09 00 b9 01 ................H......H...;....
13300 00 00 00 ff 15 c7 b5 03 00 48 89 05 28 4c 09 00 48 85 c0 0f 84 3b 0a 00 00 48 8b 15 b8 3d 09 00 .........H..(L..H....;...H...=..
13320 b9 01 00 00 00 ff 15 a5 b5 03 00 48 89 05 9e 4c 09 00 48 85 c0 0f 84 19 0a 00 00 4c 8b 05 ee 4b ...........H...L..H........L...K
13340 09 00 b9 02 00 00 00 48 8b 15 6a 46 09 00 ff 15 7c b5 03 00 48 89 05 15 47 09 00 48 85 c0 0f 84 .......H..jF....|...H...G..H....
13360 f0 09 00 00 48 8b 15 ad 3c 09 00 b9 01 00 00 00 ff 15 5a b5 03 00 48 89 05 8b 4f 09 00 48 85 c0 ....H...<.........Z...H...O..H..
13380 0f 84 ce 09 00 00 48 8b 15 d3 37 09 00 b9 01 00 00 00 ff 15 38 b5 03 00 48 89 05 b9 4f 09 00 48 ......H...7.........8...H...O..H
133a0 85 c0 0f 84 ac 09 00 00 48 8b 15 c1 34 09 00 b9 01 00 00 00 ff 15 16 b5 03 00 48 89 05 0f 4d 09 ........H...4.............H...M.
133c0 00 48 85 c0 0f 84 8a 09 00 00 48 8b 15 df 36 09 00 b9 01 00 00 00 ff 15 f4 b4 03 00 48 89 05 7d .H........H...6.............H..}
133e0 47 09 00 48 85 c0 0f 84 68 09 00 00 48 8b 15 c5 35 09 00 b9 01 00 00 00 ff 15 d2 b4 03 00 48 89 G..H....h...H...5.............H.
13400 05 fb 48 09 00 48 85 c0 0f 84 46 09 00 00 48 8b 15 d3 34 09 00 b9 01 00 00 00 ff 15 b0 b4 03 00 ..H..H....F...H...4.............
13420 48 89 05 69 43 09 00 48 85 c0 0f 84 24 09 00 00 48 8b 15 59 37 09 00 b9 01 00 00 00 ff 15 8e b4 H..iC..H....$...H..Y7...........
13440 03 00 48 89 05 cf 45 09 00 48 85 c0 0f 84 02 09 00 00 48 8b 15 b7 3e 09 00 b9 01 00 00 00 ff 15 ..H...E..H........H...>.........
13460 6c b4 03 00 48 89 05 95 46 09 00 48 85 c0 0f 84 e0 08 00 00 48 8b 15 45 3c 09 00 b9 01 00 00 00 l...H...F..H........H..E<.......
13480 ff 15 4a b4 03 00 48 89 05 a3 46 09 00 48 85 c0 0f 84 be 08 00 00 48 8b 15 9b 35 09 00 b9 01 00 ..J...H...F..H........H...5.....
134a0 00 00 ff 15 28 b4 03 00 48 89 05 29 49 09 00 48 85 c0 0f 84 9c 08 00 00 48 8b 15 89 b6 03 00 b9 ....(...H..)I..H........H.......
134c0 03 00 00 00 4c 8b ca 4c 8b c2 ff 15 00 b4 03 00 48 89 05 49 4c 09 00 48 85 c0 0f 84 74 08 00 00 ....L..L........H..IL..H....t...
134e0 48 8b 15 d1 43 09 00 b9 01 00 00 00 ff 15 de b3 03 00 48 89 05 2f 49 09 00 48 85 c0 0f 84 52 08 H...C.............H../I..H....R.
13500 00 00 48 8b 15 cf 3a 09 00 b9 01 00 00 00 ff 15 bc b3 03 00 48 89 05 dd 49 09 00 48 85 c0 0f 84 ..H...:.............H...I..H....
13520 30 08 00 00 48 8b 15 35 3f 09 00 b9 01 00 00 00 ff 15 9a b3 03 00 48 89 05 9b 45 09 00 48 85 c0 0...H..5?.............H...E..H..
13540 0f 84 0e 08 00 00 48 8b 15 9b 39 09 00 b9 01 00 00 00 ff 15 78 b3 03 00 48 89 05 09 4a 09 00 48 ......H...9.........x...H...J..H
13560 85 c0 0f 84 ec 07 00 00 48 8b 15 c1 36 09 00 b9 01 00 00 00 ff 15 56 b3 03 00 48 89 05 b7 4d 09 ........H...6.........V...H...M.
13580 00 48 85 c0 0f 84 ca 07 00 00 48 8b 15 c7 37 09 00 b9 01 00 00 00 ff 15 34 b3 03 00 48 89 05 d5 .H........H...7.........4...H...
135a0 4a 09 00 48 85 c0 0f 84 a8 07 00 00 48 8b 15 3d 3d 09 00 b9 01 00 00 00 ff 15 12 b3 03 00 48 89 J..H........H..==.............H.
135c0 05 33 47 09 00 48 85 c0 0f 84 86 07 00 00 48 8b 15 e3 3a 09 00 b9 01 00 00 00 ff 15 f0 b2 03 00 .3G..H........H...:.............
135e0 48 89 05 11 44 09 00 48 85 c0 0f 84 64 07 00 00 48 8b 15 e9 34 09 00 b9 01 00 00 00 ff 15 ce b2 H...D..H....d...H...4...........
13600 03 00 48 89 05 df 49 09 00 48 85 c0 0f 84 42 07 00 00 48 8b 15 4f 33 09 00 b9 01 00 00 00 ff 15 ..H...I..H....B...H..O3.........
13620 ac b2 03 00 48 89 05 b5 42 09 00 48 85 c0 0f 84 20 07 00 00 48 8b 15 0d 3a 09 00 b9 01 00 00 00 ....H...B..H........H...:.......
13640 ff 15 8a b2 03 00 48 89 05 73 40 09 00 48 85 c0 0f 84 fe 06 00 00 48 8b 0d eb b4 03 00 4c 8b c1 ......H..s@..H........H......L..
13660 48 8b d1 ff 15 ff b0 03 00 48 89 05 98 3f 09 00 48 85 c0 0f 84 db 06 00 00 48 8b 15 80 36 09 00 H........H...?..H........H...6..
13680 b9 01 00 00 00 ff 15 45 b2 03 00 48 89 05 d6 42 09 00 48 85 c0 0f 84 b9 06 00 00 4c 8b 05 7e 42 .......E...H...B..H........L..~B
136a0 09 00 b9 02 00 00 00 48 8b 15 9a 3e 09 00 ff 15 1c b2 03 00 48 89 05 e5 40 09 00 48 85 c0 0f 84 .......H...>........H...@..H....
136c0 90 06 00 00 48 8b 15 7d 3e 09 00 b9 01 00 00 00 ff 15 fa b1 03 00 48 89 05 cb 46 09 00 48 85 c0 ....H..}>.............H...F..H..
136e0 0f 84 6e 06 00 00 48 8b 15 8b 39 09 00 b9 01 00 00 00 ff 15 d8 b1 03 00 48 89 05 71 41 09 00 48 ..n...H...9.............H..qA..H
13700 85 c0 0f 84 4c 06 00 00 48 8b 15 61 3c 09 00 b9 01 00 00 00 ff 15 b6 b1 03 00 48 89 05 7f 41 09 ....L...H..a<.............H...A.
13720 00 48 85 c0 0f 84 2a 06 00 00 48 8b 15 df 3d 09 00 b9 01 00 00 00 ff 15 94 b1 03 00 48 89 05 45 .H....*...H...=.............H..E
13740 4b 09 00 48 85 c0 0f 84 08 06 00 00 48 8b 15 a5 3d 09 00 b9 01 00 00 00 ff 15 72 b1 03 00 48 89 K..H........H...=.........r...H.
13760 05 db 44 09 00 48 85 c0 0f 84 e6 05 00 00 48 8b 15 2b 32 09 00 b9 01 00 00 00 ff 15 50 b1 03 00 ..D..H........H..+2.........P...
13780 48 89 05 89 42 09 00 48 85 c0 0f 84 c4 05 00 00 48 8b 15 a9 3c 09 00 b9 01 00 00 00 ff 15 2e b1 H...B..H........H...<...........
137a0 03 00 48 89 05 9f 46 09 00 48 85 c0 0f 84 a2 05 00 00 48 8b 15 1f 33 09 00 b9 01 00 00 00 ff 15 ..H...F..H........H...3.........
137c0 0c b1 03 00 48 89 05 15 49 09 00 48 85 c0 0f 84 80 05 00 00 48 8b 15 c5 3b 09 00 b9 01 00 00 00 ....H...I..H........H...;.......
137e0 ff 15 ea b0 03 00 48 89 05 b3 48 09 00 48 85 c0 0f 84 5e 05 00 00 48 8b 15 bb 30 09 00 b9 01 00 ......H...H..H....^...H...0.....
13800 00 00 ff 15 c8 b0 03 00 48 89 05 71 45 09 00 48 85 c0 0f 84 3c 05 00 00 48 8b 15 69 30 09 00 b9 ........H..qE..H....<...H..i0...
13820 01 00 00 00 ff 15 a6 b0 03 00 48 89 05 df 3d 09 00 48 85 c0 0f 84 1a 05 00 00 4c 8b 05 df b2 03 ..........H...=..H........L.....
13840 00 b9 02 00 00 00 48 8b 15 6b 41 09 00 ff 15 7d b0 03 00 48 89 05 c6 42 09 00 48 85 c0 0f 84 f1 ......H..kA....}...H...B..H.....
13860 04 00 00 48 8b 15 b6 33 09 00 b9 01 00 00 00 ff 15 5b b0 03 00 48 89 05 3c 3d 09 00 48 85 c0 0f ...H...3.........[...H..<=..H...
13880 84 cf 04 00 00 48 8b 15 f4 36 09 00 b9 01 00 00 00 ff 15 39 b0 03 00 48 89 05 ba 47 09 00 48 85 .....H...6.........9...H...G..H.
138a0 c0 0f 84 ad 04 00 00 48 8b 15 82 3a 09 00 b9 01 00 00 00 ff 15 17 b0 03 00 48 89 05 78 3f 09 00 .......H...:.............H..x?..
138c0 48 85 c0 0f 84 8b 04 00 00 48 8b 15 20 37 09 00 b9 01 00 00 00 ff 15 f5 af 03 00 48 89 05 2e 4a H........H...7.............H...J
138e0 09 00 48 85 c0 0f 84 69 04 00 00 48 8b 15 4e 33 09 00 b9 01 00 00 00 ff 15 d3 af 03 00 48 89 05 ..H....i...H..N3.............H..
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13920 89 05 22 47 09 00 48 85 c0 0f 84 25 04 00 00 48 8b 15 9a 2f 09 00 b9 01 00 00 00 ff 15 8f af 03 .."G..H....%...H.../............
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13960 af 03 00 48 89 05 ee 43 09 00 48 85 c0 0f 84 e1 03 00 00 48 8b 15 76 3b 09 00 b9 01 00 00 00 ff ...H...C..H........H..v;........
13980 15 4b af 03 00 48 89 05 54 40 09 00 48 85 c0 0f 84 bf 03 00 00 48 8b 15 54 3b 09 00 b9 01 00 00 .K...H..T@..H........H..T;......
139a0 00 ff 15 29 af 03 00 48 89 05 2a 42 09 00 48 85 c0 0f 84 9d 03 00 00 48 8b 15 aa 33 09 00 b9 01 ...)...H..*B..H........H...3....
139c0 00 00 00 ff 15 07 af 03 00 48 89 05 d8 42 09 00 48 85 c0 0f 84 7b 03 00 00 48 8b 15 10 34 09 00 .........H...B..H....{...H...4..
139e0 b9 01 00 00 00 ff 15 e5 ae 03 00 48 89 05 6e 45 09 00 48 85 c0 0f 84 59 03 00 00 48 8b 15 3e 30 ...........H..nE..H....Y...H..>0
13a00 09 00 b9 01 00 00 00 ff 15 c3 ae 03 00 48 89 05 74 45 09 00 48 85 c0 0f 84 37 03 00 00 48 8b 15 .............H..tE..H....7...H..
13a20 9c 34 09 00 b9 01 00 00 00 ff 15 a1 ae 03 00 48 89 05 52 42 09 00 48 85 c0 0f 84 15 03 00 00 b9 .4.............H..RB..H.........
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13c00 01 00 00 48 8b 15 0e 36 09 00 b9 01 00 00 00 ff 15 bb ac 03 00 48 89 05 34 3d 09 00 48 85 c0 0f ...H...6.............H..4=..H...
13c20 84 2f 01 00 00 48 8b 15 3c 36 09 00 b9 01 00 00 00 ff 15 99 ac 03 00 48 89 05 52 3c 09 00 48 85 ./...H..<6.............H..R<..H.
13c40 c0 0f 84 0d 01 00 00 48 8b 15 fa 31 09 00 b9 01 00 00 00 ff 15 77 ac 03 00 48 89 05 08 44 09 00 .......H...1.........w...H...D..
13c60 48 85 c0 0f 84 eb 00 00 00 48 8b 15 e0 2c 09 00 b9 01 00 00 00 ff 15 55 ac 03 00 48 89 05 5e 47 H........H...,.........U...H..^G
13c80 09 00 48 85 c0 0f 84 c9 00 00 00 48 8b 05 d6 34 09 00 b9 05 00 00 00 4c 8b 0d da 35 09 00 4c 8b ..H........H...4.......L...5..L.
13ca0 05 73 38 09 00 48 8b 15 ac 35 09 00 48 89 44 24 28 48 8b 05 d0 35 09 00 48 89 44 24 20 ff 15 0d .s8..H...5..H.D$(H...5..H.D$....
13cc0 ac 03 00 48 89 05 e6 46 09 00 48 85 c0 0f 84 81 00 00 00 4c 8b 0d 16 44 09 00 48 8b 15 f7 35 09 ...H...F..H........L...D..H...5.
13ce0 00 4c 89 4c 24 70 c7 44 24 68 01 00 00 00 48 89 54 24 60 48 8b 15 0e 31 09 00 48 89 54 24 58 48 .L.L$p.D$h....H.T$`H...1..H.T$XH
13d00 8b 15 b2 3b 09 00 48 89 54 24 50 48 89 54 24 48 48 89 44 24 40 48 89 54 24 38 48 89 54 24 30 33 ...;..H.T$PH.T$HH.D$@H.T$8H.T$03
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13d40 05 db 3f 09 00 48 85 c0 74 0a 33 c0 48 81 c4 88 00 00 00 c3 b8 ff ff ff ff 48 81 c4 88 00 00 00 ..?..H..t.3.H............H......
13d60 c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc 48 89 5c 24 08 57 48 83 ec 20 48 8b 0d 17 45 09 ................H.\$.WH...H...E.
13d80 00 48 8b 3d 78 2c 09 00 48 8b d7 48 8b 41 08 4c 8b 80 90 00 00 00 4d 85 c0 74 05 41 ff d0 eb 06 .H.=x,..H..H.A.L......M..t.A....
13da0 ff 15 d2 ad 03 00 48 8b d8 48 85 c0 75 1a 48 8b 0d 13 ab 03 00 48 8d 15 8c e8 08 00 4c 8b c7 48 ......H..H..u.H......H......L..H
13dc0 8b 09 ff 15 b8 ac 03 00 48 89 1d e9 44 09 00 48 85 db 0f 84 65 01 00 00 48 8b 0d 39 2c 09 00 e8 ........H...D..H....e...H..9,...
13de0 fc bb ff ff 48 89 05 f5 39 09 00 48 85 c0 0f 84 49 01 00 00 48 8b 0d fd 2d 09 00 e8 e0 bb ff ff ....H...9..H....I...H...-.......
13e00 48 89 05 d9 41 09 00 48 85 c0 0f 84 2d 01 00 00 48 8b 0d e9 34 09 00 e8 c4 bb ff ff 48 89 05 8d H...A..H....-...H...4.......H...
13e20 38 09 00 48 85 c0 0f 84 11 01 00 00 48 8b 0d f5 2d 09 00 e8 a8 bb ff ff 48 89 05 21 44 09 00 48 8..H........H...-.......H..!D..H
13e40 85 c0 0f 84 f5 00 00 00 48 8b 0d d9 2b 09 00 e8 8c bb ff ff 48 89 05 a5 3a 09 00 48 85 c0 0f 84 ........H...+.......H...:..H....
13e60 d9 00 00 00 48 8b 0d d5 36 09 00 e8 70 bb ff ff 48 89 05 a9 3a 09 00 48 85 c0 0f 84 bd 00 00 00 ....H...6...p...H...:..H........
13e80 48 8b 0d 21 36 09 00 e8 54 bb ff ff 48 89 05 6d 39 09 00 48 85 c0 0f 84 a1 00 00 00 48 8b 0d 95 H..!6...T...H..m9..H........H...
13ea0 33 09 00 e8 38 bb ff ff 48 89 05 59 45 09 00 48 85 c0 0f 84 85 00 00 00 48 8b 0d e9 31 09 00 e8 3...8...H..YE..H........H...1...
13ec0 1c bb ff ff 48 89 05 6d 3a 09 00 48 85 c0 74 6d 48 8b 0d e9 2b 09 00 e8 04 bb ff ff 48 89 05 9d ....H..m:..H..tmH...+.......H...
13ee0 43 09 00 48 85 c0 74 55 48 8b 0d 01 2d 09 00 e8 ec ba ff ff 48 89 05 3d 41 09 00 48 85 c0 74 3d C..H..tUH...-.......H..=A..H..t=
13f00 48 8b 0d f9 30 09 00 e8 d4 ba ff ff 48 89 05 d5 3d 09 00 48 85 c0 74 25 48 8b 0d 29 29 09 00 e8 H...0.......H...=..H..t%H..))...
13f20 bc ba ff ff 48 89 05 85 39 09 00 48 85 c0 74 0d 33 c0 48 8b 5c 24 30 48 83 c4 20 5f c3 48 8b 5c ....H...9..H..t.3.H.\$0H..._.H.\
13f40 24 30 b8 ff ff ff ff 48 83 c4 20 5f c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc $0.....H..._....................
13f60 48 8b 81 78 01 00 00 48 ff 00 48 8b 81 78 01 00 00 c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc H..x...H..H..x..................
13f80 40 53 48 83 ec 20 48 8b 05 bb ab 03 00 48 8b d9 48 8b 49 18 48 89 43 18 48 8b 05 a9 ab 03 00 48 @SH...H......H..H.I.H.C.H......H
13fa0 ff 00 48 85 c9 74 0c 48 83 29 01 75 06 ff 15 55 aa 03 00 48 8b 05 8e ab 03 00 48 8b 4b 20 48 89 ..H..t.H.).u...U...H......H.K.H.
13fc0 43 20 48 8b 05 7f ab 03 00 48 ff 00 48 85 c9 74 0c 48 83 29 01 75 06 ff 15 2b aa 03 00 48 8b 05 C.H......H..H..t.H.).u...+...H..
13fe0 64 ab 03 00 48 8b 4b 28 48 89 43 28 48 8b 05 55 ab 03 00 48 ff 00 48 85 c9 74 0c 48 83 29 01 75 d...H.K(H.C(H..U...H..H..t.H.).u
14000 06 ff 15 01 aa 03 00 48 8b 4b 50 48 85 c9 74 14 48 c7 43 50 00 00 00 00 48 83 29 01 75 06 ff 15 .......H.KPH..t.H.CP....H.).u...
14020 e4 a9 03 00 48 8b 05 1d ab 03 00 48 8b 8b 78 01 00 00 48 89 83 78 01 00 00 48 8b 05 08 ab 03 00 ....H......H..x...H..x...H......
14040 48 ff 00 48 85 c9 74 0c 48 83 29 01 75 06 ff 15 b4 a9 03 00 48 8d 8b a8 00 00 00 41 b8 1b 9e 00 H..H..t.H.).u.......H......A....
14060 00 e8 0a 93 ff ff 33 c0 48 83 c4 20 5b c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc ......3.H...[...................
14080 48 89 5c 24 08 48 89 74 24 10 57 48 83 ec 20 48 8b d9 49 8b f8 48 8b 49 18 48 8b f2 48 85 c9 74 H.\$.H.t$.WH...H..I..H.I.H..H..t
140a0 09 49 8b d0 ff d6 85 c0 75 4d 48 8b 4b 20 48 85 c9 74 09 48 8b d7 ff d6 85 c0 75 3b 48 8b 4b 28 .I......uMH.K.H..t.H......u;H.K(
140c0 48 85 c9 74 09 48 8b d7 ff d6 85 c0 75 29 48 8b 4b 50 48 85 c9 74 09 48 8b d7 ff d6 85 c0 75 17 H..t.H......u)H.KPH..t.H......u.
140e0 48 8b 8b 78 01 00 00 48 85 c9 74 09 48 8b d7 ff d6 85 c0 75 02 33 c0 48 8b 5c 24 30 48 8b 74 24 H..x...H..t.H......u.3.H.\$0H.t$
14100 38 48 83 c4 20 5f c3 cc cc cc cc cc cc cc cc cc 40 53 48 83 ec 20 48 8b 41 08 48 8b d9 f6 80 a8 8H..._..........@SH...H.A.H.....
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14140 a6 03 00 85 c0 0f 85 84 00 00 00 48 8b cb ff 15 74 aa 03 00 4c 8d 44 24 30 48 8d 54 24 38 48 8d ...........H....t...L.D$0H.T$8H.
14160 4c 24 40 ff 15 1f a7 03 00 48 ff 03 48 8d 8b a8 00 00 00 41 b8 a9 8b 00 00 e8 f2 91 ff ff 4c 8b L$@......H..H......A..........L.
14180 44 24 30 48 8b 54 24 38 48 8b 4c 24 40 48 ff 0b ff 15 82 a8 03 00 48 8b 8b 78 01 00 00 48 85 c9 D$0H.T$8H.L$@H........H..x...H..
141a0 74 17 48 c7 83 78 01 00 00 00 00 00 00 48 83 29 01 75 06 ff 15 4f a8 03 00 48 8b cb ff 15 b6 a6 t.H..x.......H.).u...O...H......
141c0 03 00 48 8b cb 48 83 c4 20 5b e9 e1 07 00 00 48 83 c4 20 5b c3 cc cc cc cc cc cc cc cc cc cc cc ..H..H...[.....H...[............
141e0 48 89 5c 24 08 48 89 74 24 10 57 48 83 ec 20 f7 81 a8 00 00 00 00 00 10 00 49 8b f8 48 8b f2 75 H.\$.H.t$.WH.............I..H..u
14200 0a 33 d2 ff 91 30 01 00 00 eb 17 48 8b 05 f6 aa 03 00 45 33 c0 48 8b 15 9c 36 09 00 ff 90 38 01 .3...0.....H......E3.H...6....8.
14220 00 00 48 8b d8 48 85 c0 74 73 48 8b 05 c7 3e 09 00 4c 8b c7 48 89 43 10 48 8b d6 48 8b 05 06 a9 ..H..H..tsH...>..L..H.C.H..H....
14240 03 00 48 8b cb 48 89 43 18 48 8b 05 f8 a8 03 00 48 ff 00 48 8b 05 ee a8 03 00 48 89 43 20 48 8b ..H..H.C.H......H..H......H.C.H.
14260 05 e3 a8 03 00 48 ff 00 48 8b 05 d9 a8 03 00 48 89 43 28 48 8b 05 ce a8 03 00 48 ff 00 48 c7 43 .....H..H......H.C(H......H..H.C
14280 50 00 00 00 00 e8 26 b0 00 00 85 c0 79 21 48 83 2b 01 75 09 48 8b cb ff 15 6b a7 03 00 33 c0 48 P.....&.....y!H.+.u.H....k...3.H
142a0 8b 5c 24 30 48 8b 74 24 38 48 83 c4 20 5f c3 48 8b 05 d2 3e 09 00 48 8b 74 24 38 48 89 43 10 48 .\$0H.t$8H..._.H...>..H.t$8H.C.H
142c0 8b 05 82 a8 03 00 48 89 83 78 01 00 00 48 8b 05 74 a8 03 00 48 ff 00 48 8b c3 48 c7 83 a8 00 00 ......H..x...H..t...H..H..H.....
142e0 00 00 00 00 00 48 8b 5c 24 30 48 83 c4 20 5f c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc .....H.\$0H..._.................
14300 40 55 41 56 48 83 ec 28 48 89 5c 24 40 45 33 f6 48 89 74 24 48 41 8b de 48 89 7c 24 50 41 8b ee @UAVH..(H.\$@E3.H.t$HA..H.|$PA..
14320 48 8b 79 20 48 3b 3d 1d a8 03 00 4c 89 64 24 58 4c 89 7c 24 20 4c 8b f9 0f 85 a2 00 00 00 48 8b H.y.H;=....L.d$XL.|$.L........H.
14340 1d 43 3d 09 00 48 ff 03 48 8b 79 78 48 63 41 6c 48 8b 13 4c 8d 24 c7 49 3b fc 73 66 0f 1f 40 00 .C=..H..H.yxHcAlH..L.$.I;.sf..@.
14360 48 8b 0f ff 15 b7 a8 03 00 48 8b f0 48 85 c0 0f 84 cc 00 00 00 48 8b cd 48 8b e8 48 85 c9 74 0c H........H..H........H..H..H..t.
14380 48 83 29 01 75 06 ff 15 7c a6 03 00 48 8b d6 48 8b cb ff 15 c0 a3 03 00 48 8b f0 48 85 c0 0f 84 H.).u...|...H..H........H..H....
143a0 90 00 00 00 48 8b cb 48 8b d8 48 83 29 01 75 06 ff 15 52 a6 03 00 48 83 c7 08 49 3b fc 72 a1 48 ....H..H..H.).u...R...H...I;.r.H
143c0 8b 16 48 8d 42 01 48 8b fb 48 89 03 49 8b 4f 20 48 83 29 01 75 06 ff 15 2c a6 03 00 49 89 5f 20 ..H.B.H..H..I.O.H.).u...,...I._.
143e0 48 ff 07 4d 8b 77 20 4c 8b 7c 24 20 4c 8b 64 24 58 48 8b 7c 24 50 48 8b 74 24 48 48 85 db 74 0f H..M.w.L.|$.L.d$XH.|$PH.t$HH..t.
14400 48 83 2b 01 75 09 48 8b cb ff 15 f9 a5 03 00 48 8b 5c 24 40 48 85 ed 74 10 48 83 6d 00 01 75 09 H.+.u.H........H.\$@H..t.H.m..u.
14420 48 8b cd ff 15 df a5 03 00 49 8b c6 48 83 c4 28 41 5e 5d c3 ba a9 7e 00 00 41 b8 57 02 00 00 eb H........I..H..(A^]...~..A.W....
14440 0b ba 9d 7e 00 00 41 b8 56 02 00 00 4c 8b 0d 15 2b 04 00 48 8d 0d 86 f9 08 00 e8 01 74 ff ff eb ...~..A.V...L...+..H........t...
14460 86 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc 48 89 5c 24 18 57 48 83 ec 20 48 8b 41 08 48 8b ................H.\$.WH...H.A.H.
14480 d9 48 8b 15 20 29 09 00 4c 8b 80 90 00 00 00 4d 85 c0 74 05 41 ff d0 eb 06 ff 15 d9 a6 03 00 48 .H...)..L......M..t.A..........H
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144c0 8b 4b 60 ff 15 57 a7 03 00 48 8b d8 48 85 c0 75 07 bd 3a 7e 00 00 eb 19 48 8b d3 48 8b cf ff 15 .K`..W...H..H..u..:~....H..H....
144e0 f4 a5 03 00 48 8b f0 48 85 c0 75 4a bd 3c 7e 00 00 48 8b 35 70 2a 04 00 48 83 2f 01 75 09 48 8b ....H..H..uJ.<~..H.5p*..H./.u.H.
14500 cf ff 15 01 a5 03 00 48 85 db 74 0f 48 83 2b 01 75 09 48 8b cb ff 15 ed a4 03 00 4c 8b ce 48 8d .......H..t.H.+.u.H........L..H.
14520 0d e3 f8 08 00 41 b8 4f 02 00 00 8b d5 e8 2e 73 ff ff 33 c0 eb 21 48 83 2f 01 75 09 48 8b cf ff .....A.O.......s..3..!H./.u.H...
14540 15 c3 a4 03 00 48 83 2b 01 75 09 48 8b cb ff 15 b4 a4 03 00 48 8b c6 48 8b 74 24 38 48 8b 6c 24 .....H.+.u.H........H..H.t$8H.l$
14560 30 48 8b 5c 24 40 48 83 c4 20 5f c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc 0H.\$@H..._.....................
14580 48 83 ec 28 48 8b 49 60 ff 15 92 a6 03 00 48 85 c0 75 20 4c 8b 0d ce 29 04 00 48 8d 0d 97 f8 08 H..(H.I`......H..u.L...)..H.....
145a0 00 ba f7 7d 00 00 41 b8 4b 02 00 00 e8 af 72 ff ff 33 c0 48 83 c4 28 c3 cc cc cc cc cc cc cc cc ...}..A.K.....r..3.H..(.........
145c0 48 83 ec 28 8b 49 6c 89 4c 24 30 ff 15 ff a5 03 00 48 85 c0 75 20 4c 8b 0d 8b 29 04 00 48 8d 0d H..(.Il.L$0......H..u.L...)..H..
145e0 84 f8 08 00 ba b8 7d 00 00 41 b8 47 02 00 00 e8 6c 72 ff ff 33 c0 48 83 c4 28 c3 cc cc cc cc cc ......}..A.G....lr..3.H..(......
14600 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc e9 1b 7c 00 00 cc cc cc cc cc cc cc cc cc cc cc ..................|.............
14620 e9 eb 7d 00 00 cc cc cc cc cc cc cc cc cc cc cc 48 89 5c 24 08 48 89 6c 24 10 48 89 74 24 18 57 ..}.............H.\$.H.l$.H.t$.W
14640 48 83 ec 20 48 8b d9 33 c9 ff 15 11 a1 03 00 48 8b f8 48 85 c0 75 11 48 8b 35 0a 29 04 00 bd 84 H...H..3.......H..H..u.H.5.)....
14660 7c 00 00 e9 b4 00 00 00 48 8b 73 78 48 63 43 6c 48 8d 2c c6 48 3b f5 73 63 0f 1f 80 00 00 00 00 |.......H.sxHcClH.,.H;.sc.......
14680 48 8b 0e ff 15 97 a5 03 00 48 8b d8 48 85 c0 0f 84 a9 00 00 00 48 8b 4f 10 48 39 4f 20 7e 15 48 H........H..H........H.O.H9O.~.H
146a0 ff 00 48 8b 47 18 48 89 1c c8 48 8d 41 01 48 89 47 10 eb 10 48 8b d3 48 8b cf ff 15 d8 a0 03 00 ..H.G.H...H.A.H.G...H..H........
146c0 85 c0 75 73 48 83 2b 01 75 09 48 8b cb ff 15 35 a3 03 00 48 83 c6 08 48 3b f5 72 a4 48 8b cf ff ..usH.+.u.H....5...H...H;.r.H...
146e0 15 0b a2 03 00 48 8b d8 48 85 c0 75 58 bd 8f 7c 00 00 48 8b 35 6f 28 04 00 48 83 2f 01 75 09 48 .....H..H..uX..|..H.5o(..H./.u.H
14700 8b cf ff 15 00 a3 03 00 48 85 db 74 0f 48 83 2b 01 75 09 48 8b cb ff 15 ec a2 03 00 4c 8b ce 48 ........H..t.H.+.u.H........L..H
14720 8d 0d ca f7 08 00 41 b8 34 02 00 00 8b d5 e8 2d 71 ff ff 33 c0 eb 20 bd 8c 7c 00 00 eb b4 bd 8a ......A.4......-q..3.....|......
14740 7c 00 00 eb ad 48 83 2f 01 75 09 48 8b cf ff 15 b4 a2 03 00 48 8b c3 48 8b 5c 24 30 48 8b 6c 24 |....H./.u.H........H..H.\$0H.l$
14760 38 48 8b 74 24 40 48 83 c4 20 5f c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc 8H.t$@H..._.....................
14780 48 8b 41 18 48 ff 00 48 8b 41 18 c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc H.A.H..H.A......................
147a0 e9 1b 81 00 00 cc cc cc cc cc cc cc cc cc cc cc 48 83 ec 28 4d 85 c0 74 09 48 83 c4 28 e9 fe 9e ................H..(M..t.H..(...
147c0 00 00 4c 8b 41 08 48 8d 15 8b ee 08 00 48 8b 0d 44 a5 03 00 4d 8b 40 18 48 8b 09 ff 15 9f a2 03 ..L.A.H......H..D...M.@.H.......
147e0 00 b8 ff ff ff ff 48 83 c4 28 c3 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc ......H..(......................
14800 48 89 5c 24 08 57 48 83 ec 20 48 8b f9 48 8b ca ff 15 0a a4 03 00 48 8b d8 48 85 c0 75 0b 48 8b H.\$.WH...H..H........H..H..u.H.
14820 5c 24 30 48 83 c4 20 5f c3 48 8b 47 08 48 8b d3 48 8b cf 4c 8b 40 70 41 ff 50 08 48 83 2b 01 48 \$0H..._.H.G.H..H..L.@pA.P.H.+.H
14840 8b f8 75 09 48 8b cb ff 15 bb a1 03 00 48 8b 5c 24 30 48 8b c7 48 83 c4 20 5f c3 cc cc cc cc cc ..u.H........H.\$0H..H..._......
14860 cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc cc 40 53 48 83 ec 20 48 8b 05 cb a2 03 00 48 8b d9 ................@SH...H......H..
14880 48 8b 49 18 48 89 43 18 48 8b 05 b9 a2 03 00 48 ff 00 48 85 c9 74 0c 48 83 29 01 75 06 ff 15 65 H.I.H.C.H......H..H..t.H.).u...e
148a0 a1 03 00 48 8b 05 9e a2 03 00 48 8b 4b 20 48 89 43 20 48 8b 05 8f a2 03 00 48 ff 00 48 85 c9 74 ...H......H.K.H.C.H......H..H..t
148c0 0c 48 83 29 01 75 06 ff 15 3b a1 03 00 48 8b 05 74 a2 03 00 48 8b 4b 28 48 89 43 28 48 8b 05 65 .H.).u...;...H..t...H.K(H.C(H..e
148e0 a2 03 00 48 ff 00 48 85 c9 74 0c 48 83 29 01 75 06 ff 15 11 a1 03 00 48 8b 4b 50 48 85 c9 74 14 ...H..H..t.H.).u.......H.KPH..t.
14900 48 c7 43 50 00 00 00 00 48 83 29 01 75 06 ff 15 f4 a0 03 00 33 c0 48 83 c4 20 5b c3 cc cc cc cc H.CP....H.).u.......3.H...[.....
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32980 f5 b9 01 00 00 00 ff 15 d4 bd 01 00 48 8b e8 48 85 c0 75 19 48 8b 3d bd 45 02 00 bb 2c 0e 00 00 ............H..H..u.H.=.E...,...
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32ac0 ff 75 0f bb 2d 0e 00 00 be 6d 43 00 00 e9 f4 22 00 00 48 83 6d 00 01 75 09 48 8b cd ff 15 26 bf .u..-....mC...."..H.m..u.H....&.
32ae0 01 00 49 8b 47 08 48 8b 0d 73 bf 01 00 48 3b c1 0f 84 25 01 00 00 48 3b 05 43 bd 01 00 0f 84 18 ..I.G.H..s...H;...%...H;.C......
32b00 01 00 00 49 8b cf ff 15 ac bf 01 00 48 89 44 24 58 48 8b f0 48 85 c0 75 19 48 8b 3d 38 44 02 00 ...I........H.D$XH..H..u.H.=8D..
32b20 bb 2d 0e 00 00 be 90 43 00 00 49 8b ee e9 ce 22 00 00 49 83 2f 01 75 09 49 8b cf ff 15 c7 be 01 .-.....C..I...."..I./.u.I.......
32b40 00 48 8b 46 08 48 8b ce 4d 8b fe 49 8b de 48 8b b8 e0 00 00 00 ff d7 48 8b e8 48 85 c0 74 60 48 .H.F.H..M..I..H........H..H..t`H
32b60 8b ce bb 01 00 00 00 ff d7 4c 8b e0 48 85 c0 74 4e 48 8b ce bb 02 00 00 00 ff d7 4c 8b e8 48 85 .........L..H..tNH.........L..H.
32b80 c0 74 3c 48 8b ce ff d7 48 8b c8 8d 53 01 e8 7d ac fd ff 85 c0 79 0f bb 2d 0e 00 00 be 9a 43 00 .t<H....H...S..}.....y..-.....C.
32ba0 00 e9 20 22 00 00 48 83 2e 01 75 09 48 8b ce ff 15 53 be 01 00 4c 89 74 24 58 e9 0f 01 00 00 48 ..."..H...u.H....S...L.t$X.....H
32bc0 83 2e 01 75 09 48 8b ce ff 15 3a be 01 00 4c 89 74 24 58 e8 88 ac fd ff 85 c0 75 30 48 8b 0d b5 ...u.H....:...L.t$X.......u0H...
32be0 be 01 00 48 8d 05 d5 4b 07 00 48 83 fb 01 4c 8d 0d 97 ec 06 00 4c 8b c3 48 8d 15 91 f6 06 00 4c ...H...K..H...L......L..H......L
32c00 0f 44 c8 48 8b 09 ff 15 74 be 01 00 bb 2d 0e 00 00 be a2 43 00 00 e9 ab 21 00 00 4d 8b 47 10 49 .D.H....t....-.....C....!..M.G.I
32c20 83 f8 03 74 6c 7e 1f 48 8b 0d 6a be 01 00 48 8d 15 83 f6 06 00 41 b8 03 00 00 00 48 8b 09 ff 15 ...tl~.H..j...H......A.....H....
32c40 3c be 01 00 eb 32 4d 85 c0 78 2d 48 8b 0d 46 be 01 00 48 8d 05 66 4b 07 00 49 83 f8 01 4c 8d 0d <....2M..x-H..F...H..fK..I...L..
32c60 28 ec 06 00 48 8d 15 25 f6 06 00 4c 0f 44 c8 48 8b 09 ff 15 08 be 01 00 48 8b 3d d9 42 02 00 bb (...H..%...L.D.H........H.=.B...
32c80 2d 0e 00 00 be 76 43 00 00 49 8b ee e9 56 21 00 00 4d 8b 6f 18 48 3b c1 75 0d 4d 8b 67 20 49 8b -....vC..I...V!..M.o.H;.u.M.g.I.
32ca0 ed 4d 8b 6f 28 eb 0c 49 8b 6d 00 4d 8b 65 08 4d 8b 6d 10 48 ff 45 00 49 ff 04 24 49 ff 45 00 49 .M.o(..I.m.M.e.M.m.H.E.I..$I.E.I
32cc0 83 2f 01 75 09 49 8b cf ff 15 3a bd 01 00 4c 89 ac 24 88 00 00 00 4d 8b ec 48 89 ac 24 80 00 00 ./.u.I....:...L..$....M..H..$...
32ce0 00 4c 89 64 24 68 48 8b 1d 23 44 07 00 48 8b ac 24 c8 00 00 00 48 3b eb 0f 84 d6 03 00 00 48 8b .L.d$hH..#D..H..$....H;.......H.
32d00 05 eb ba 01 00 45 8b c6 48 39 45 08 41 8b d6 41 0f 94 c0 48 39 43 08 0f 94 c2 41 85 d0 0f 84 00 .....E..H9E.A..A...H9C....A.....
32d20 01 00 00 f6 45 20 80 75 11 48 8b cd ff 15 56 bd 01 00 85 c0 0f 88 52 02 00 00 f6 43 20 80 75 11 ....E..u.H....V.......R....C..u.
32d40 48 8b cb ff 15 3f bd 01 00 85 c0 0f 88 3b 02 00 00 4c 8b 55 10 4c 3b 53 10 0f 85 5e 01 00 00 48 H....?.......;...L.U.L;S...^...H
32d60 8b 45 18 48 8b 4b 18 48 3b c1 74 10 48 83 f8 ff 74 0a 48 83 f9 ff 0f 85 41 01 00 00 8b 4d 20 44 .E.H.K.H;.t.H...t.H.....A....M.D
32d80 8b c1 8b 53 20 8b c2 41 c1 e8 02 c1 e8 02 41 83 e0 07 83 e0 07 44 3b c0 0f 85 1f 01 00 00 b8 48 ...S...A......A......D;........H
32da0 00 00 00 f6 c1 20 74 10 f6 c1 40 b9 30 00 00 00 0f 44 c8 48 03 cd eb 04 48 8b 4d 48 f6 c2 20 74 ......t...@.0....D.H....H.MH...t
32dc0 11 f6 c2 40 ba 30 00 00 00 48 0f 44 d0 48 03 d3 eb 04 48 8b 53 48 41 83 f8 01 75 09 0f b6 01 44 ...@.0...H.D.H....H.SHA...u....D
32de0 0f b6 0a eb 14 41 83 f8 02 75 09 0f b7 01 44 0f b7 0a eb 05 8b 01 44 8b 0a 41 3b c1 0f 85 bb 00 .....A...u....D.......D..A;.....
32e00 00 00 49 83 fa 01 0f 84 c8 02 00 00 4d 0f af c2 e8 92 b1 01 00 85 c0 41 8b fe 40 0f 95 c7 e9 8c ..I.........M..........A..@.....
32e20 00 00 00 48 8b 0d 1e bd 01 00 41 8b c6 48 3b e9 0f 94 c0 85 c2 0f 85 82 00 00 00 48 3b d9 41 8b ...H......A..H;............H;.A.
32e40 c6 0f 94 c0 41 85 c0 75 74 41 b8 03 00 00 00 48 8b d3 48 8b cd ff 15 15 bc 01 00 48 8b d8 48 85 ....A..utA.....H..H........H..H.
32e60 c0 0f 84 25 01 00 00 48 3b 05 a2 ba 01 00 41 8b fe 41 8b d6 41 8b ce 40 0f 94 c7 48 3b 05 d6 bb ...%...H;.....A..A..A..@...H;...
32e80 01 00 0f 94 c2 48 3b 05 bc bc 01 00 0f 94 c1 0b d1 0b d7 75 0b 48 8b c8 ff 15 22 ba 01 00 8b f8 .....H;............u.H....".....
32ea0 48 83 2b 01 75 09 48 8b cb ff 15 59 bb 01 00 85 ff 0f 88 d5 00 00 00 0f 84 17 02 00 00 48 8b 1d H.+.u.H....Y.................H..
32ec0 44 40 07 00 48 8b 74 24 60 48 3b f3 0f 84 07 02 00 00 48 8b 05 17 b9 01 00 45 8b c6 48 39 46 08 D@..H.t$`H;.......H......E..H9F.
32ee0 41 8b d6 41 0f 94 c0 48 39 43 08 0f 94 c2 41 85 d0 0f 84 21 01 00 00 f6 46 20 80 75 11 48 8b ce A..A...H9C....A....!....F..u.H..
32f00 ff 15 82 bb 01 00 85 c0 0f 88 9d 01 00 00 f6 43 20 80 75 11 48 8b cb ff 15 6b bb 01 00 85 c0 0f ...............C..u.H....k......
32f20 88 86 01 00 00 4c 8b 56 10 4c 3b 53 10 0f 85 9a 01 00 00 48 8b 46 18 48 8b 4b 18 48 3b c1 74 10 .....L.V.L;S.......H.F.H.K.H;.t.
32f40 48 83 f8 ff 74 0a 48 83 f9 ff 0f 85 7d 01 00 00 8b 4e 20 44 8b c1 8b 53 20 8b c2 41 c1 e8 02 c1 H...t.H.....}....N.D...S...A....
32f60 e8 02 41 83 e0 07 83 e0 07 44 3b c0 0f 85 5b 01 00 00 b8 48 00 00 00 f6 c1 20 74 32 f6 c1 40 b9 ..A......D;...[....H......t2..@.
32f80 30 00 00 00 0f 44 c8 48 03 ce eb 26 48 8b 3d c5 3f 02 00 bb 38 0e 00 00 be 64 44 00 00 4d 8b fe 0....D.H...&H.=.?...8....dD..M..
32fa0 4d 8b e6 4d 8b ee 49 8b ee e9 39 1e 00 00 48 8b 4e 48 f6 c2 20 74 11 f6 c2 40 ba 30 00 00 00 48 M..M..I...9...H.NH...t...@.0...H
32fc0 0f 44 d0 48 03 d3 eb 04 48 8b 53 48 41 83 f8 01 75 09 0f b6 01 44 0f b6 0a eb 14 41 83 f8 02 75 .D.H....H.SHA...u....D.....A...u
32fe0 09 0f b7 01 44 0f b7 0a eb 05 8b 01 44 8b 0a 41 3b c1 0f 85 d5 00 00 00 49 83 fa 01 0f 84 d7 00 ....D.......D..A;.......I.......
33000 00 00 4d 0f af c2 e8 9c af 01 00 85 c0 41 8b de 0f 95 c3 e9 8f 00 00 00 48 8b 0d 29 bb 01 00 41 ..M..........A..........H..)...A
33020 8b c6 48 3b f1 0f 94 c0 85 c2 0f 85 9d 00 00 00 48 3b d9 41 8b c6 0f 94 c0 41 85 c0 0f 85 8b 00 ..H;............H;.A.....A......
33040 00 00 48 8b 15 bf 3e 07 00 41 b8 03 00 00 00 48 8b ce ff 15 18 ba 01 00 48 8b f8 48 85 c0 74 4b ..H...>..A.....H........H..H..tK
33060 48 3b 05 a9 b8 01 00 41 8b de 41 8b d6 41 8b ce 0f 94 c3 48 3b 05 ce ba 01 00 0f 94 c2 48 3b 05 H;.....A..A..A.....H;........H;.
33080 d4 b9 01 00 0f 94 c1 0b d1 0b d3 75 0b 48 8b c8 ff 15 2a b8 01 00 8b d8 48 83 2f 01 75 09 48 8b ...........u.H....*.....H./.u.H.
330a0 cf ff 15 61 b9 01 00 85 db 79 31 48 8b 3d a6 3e 02 00 bb 38 0e 00 00 be 6a 44 00 00 4d 8b fe 4d ...a.....y1H.=.>...8....jD..M..M
330c0 8b e6 4d 8b ee 49 8b ee e9 1a 1d 00 00 bb 01 00 00 00 eb 08 48 8b 74 24 60 41 8b de 4d 8b fe 85 ..M..I..............H.t$`A..M...
330e0 db 0f 84 7d 12 00 00 48 8b 1d 2a 43 07 00 48 3b eb 0f 84 3d 04 00 00 48 8b 05 f2 b6 01 00 45 8b ...}...H..*C..H;...=...H......E.
33100 c6 48 39 45 08 41 8b d6 41 0f 94 c0 48 39 43 08 0f 94 c2 41 85 d0 0f 84 00 01 00 00 f6 45 20 80 .H9E.A..A...H9C....A.........E..
33120 75 11 48 8b cd ff 15 5d b9 01 00 85 c0 0f 88 4d 02 00 00 f6 43 20 80 75 11 48 8b cb ff 15 46 b9 u.H....].......M....C..u.H....F.
33140 01 00 85 c0 0f 88 36 02 00 00 4c 8b 55 10 4c 3b 53 10 0f 85 5e 01 00 00 48 8b 45 18 48 8b 4b 18 ......6...L.U.L;S...^...H.E.H.K.
33160 48 3b c1 74 10 48 83 f8 ff 74 0a 48 83 f9 ff 0f 85 41 01 00 00 8b 4d 20 44 8b c1 8b 53 20 8b c2 H;.t.H...t.H.....A....M.D...S...
33180 41 c1 e8 02 c1 e8 02 41 83 e0 07 83 e0 07 44 3b c0 0f 85 1f 01 00 00 b8 48 00 00 00 f6 c1 20 74 A......A......D;........H......t
331a0 10 f6 c1 40 b9 30 00 00 00 0f 44 c8 48 03 cd eb 04 48 8b 4d 48 f6 c2 20 74 11 f6 c2 40 ba 30 00 ...@.0....D.H....H.MH...t...@.0.
331c0 00 00 48 0f 44 d0 48 03 d3 eb 04 48 8b 53 48 41 83 f8 01 75 09 0f b6 01 44 0f b6 0a eb 14 41 83 ..H.D.H....H.SHA...u....D.....A.
331e0 f8 02 75 09 0f b7 01 44 0f b7 0a eb 05 8b 01 44 8b 0a 41 3b c1 0f 85 bb 00 00 00 49 83 fa 01 0f ..u....D.......D..A;.......I....
33200 84 2f 03 00 00 4d 0f af c2 e8 99 ad 01 00 85 c0 41 8b fe 40 0f 95 c7 e9 8c 00 00 00 48 8b 0d 25 ./...M..........A..@........H..%
33220 b9 01 00 41 8b c6 48 3b e9 0f 94 c0 85 c2 0f 85 82 00 00 00 48 3b d9 41 8b c6 0f 94 c0 41 85 c0 ...A..H;............H;.A.....A..
33240 75 74 41 b8 03 00 00 00 48 8b d3 48 8b cd ff 15 1c b8 01 00 48 8b d8 48 85 c0 0f 84 20 01 00 00 utA.....H..H........H..H........
33260 48 3b 05 a9 b6 01 00 41 8b fe 41 8b d6 41 8b ce 40 0f 94 c7 48 3b 05 cd b8 01 00 0f 94 c2 48 3b H;.....A..A..A..@...H;........H;
33280 05 d3 b7 01 00 0f 94 c1 0b d1 0b d7 75 0b 48 8b c8 ff 15 29 b6 01 00 8b f8 48 83 2b 01 75 09 48 ............u.H....).....H.+.u.H
332a0 8b cb ff 15 60 b7 01 00 85 ff 0f 88 d0 00 00 00 0f 84 7e 02 00 00 48 8b 1d eb 35 07 00 48 3b eb ....`.............~...H...5..H;.
332c0 0f 84 6e 02 00 00 48 8b 05 23 b5 01 00 45 8b c6 48 39 45 08 41 8b d6 41 0f 94 c0 48 39 43 08 0f ..n...H..#...E..H9E.A..A...H9C..
332e0 94 c2 41 85 d0 0f 84 1f 01 00 00 f6 45 20 80 75 11 48 8b cd ff 15 8e b7 01 00 85 c0 0f 88 d4 01 ..A.........E..u.H..............
33300 00 00 f6 43 20 80 75 11 48 8b cb ff 15 77 b7 01 00 85 c0 0f 88 bd 01 00 00 4c 8b 55 10 4c 3b 53 ...C..u.H....w...........L.U.L;S
33320 10 0f 85 75 01 00 00 48 8b 45 18 48 8b 4b 18 48 3b c1 74 10 48 83 f8 ff 74 0a 48 83 f9 ff 0f 85 ...u...H.E.H.K.H;.t.H...t.H.....
33340 58 01 00 00 8b 4d 20 44 8b c1 8b 53 20 8b c2 41 c1 e8 02 c1 e8 02 41 83 e0 07 83 e0 07 44 3b c0 X....M.D...S...A......A......D;.
33360 0f 85 36 01 00 00 b8 48 00 00 00 f6 c1 20 74 2f f6 c1 40 b9 30 00 00 00 0f 44 c8 48 03 cd eb 23 ..6....H......t/..@.0....D.H...#
33380 48 8b 3d d1 3b 02 00 bb 39 0e 00 00 be 76 44 00 00 4d 8b e6 4d 8b ee 49 8b ee e9 48 1a 00 00 48 H.=.;...9....vD..M..M..I...H...H
333a0 8b 4d 48 f6 c2 20 74 11 f6 c2 40 ba 30 00 00 00 48 0f 44 d0 48 03 d3 eb 04 48 8b 53 48 41 83 f8 .MH...t...@.0...H.D.H....H.SHA..
333c0 01 75 09 0f b6 01 44 0f b6 0a eb 14 41 83 f8 02 75 09 0f b7 01 44 0f b7 0a eb 05 8b 01 44 8b 0a .u....D.....A...u....D.......D..
333e0 41 3b c1 0f 85 b3 00 00 00 49 83 fa 01 0f 84 41 01 00 00 4d 0f af c2 e8 ab ab 01 00 85 c0 41 8b A;.......I.....A...M..........A.
33400 fe 40 0f 95 c7 e9 88 00 00 00 48 8b 0d 37 b7 01 00 41 8b c6 48 3b e9 0f 94 c0 85 c2 75 7e 48 3b .@........H..7...A..H;......u~H;
33420 d9 41 8b c6 0f 94 c0 41 85 c0 75 70 41 b8 03 00 00 00 48 8b d3 48 8b cd ff 15 32 b6 01 00 48 8b .A.....A..upA.....H..H....2...H.
33440 d8 48 85 c0 0f 84 8c 00 00 00 48 3b 05 bf b4 01 00 41 8b fe 41 8b d6 41 8b ce 40 0f 94 c7 48 3b .H........H;.....A..A..A..@...H;
33460 05 f3 b5 01 00 0f 94 c2 48 3b 05 d9 b6 01 00 0f 94 c1 0b d1 0b d7 75 0b 48 8b c8 ff 15 3f b4 01 ........H;............u.H....?..
33480 00 8b f8 48 83 2b 01 75 09 48 8b cb ff 15 76 b5 01 00 85 ff 78 40 0f 84 98 00 00 00 48 8b 15 c5 ...H.+.u.H....v.....x@......H...
334a0 44 07 00 45 33 c0 48 8b 0d 33 4b 07 00 e8 ce be fd ff 4c 8b e0 48 85 c0 75 3b 48 8b 3d 97 3a 02 D..E3.H..3K.......L..H..u;H.=.:.
334c0 00 bb 3a 0e 00 00 be 88 44 00 00 4d 8b ee 49 8b ee e9 11 19 00 00 48 8b 3d 7b 3a 02 00 bb 39 0e ..:.....D..M..I.......H.={:...9.
334e0 00 00 be 7c 44 00 00 4d 8b e6 4d 8b ee 49 8b ee e9 f2 18 00 00 45 33 c9 45 33 c0 33 d2 49 8b cc ...|D..M..M..I.......E3.E3.3.I..
33500 e8 cb bc fd ff 49 83 2c 24 01 75 09 49 8b cc ff 15 f3 b4 01 00 48 8b 3d 3c 3a 02 00 4d 8b e6 bb .....I.,$.u.I........H.=<:..M...
33520 3a 0e 00 00 be 8c 44 00 00 4d 8b ee 49 8b ee e9 b3 18 00 00 48 8b 1d 85 3e 07 00 48 3b f3 0f 84 :.....D..M..I.......H...>..H;...
33540 bb 01 00 00 48 8b 05 a5 b2 01 00 45 8b c6 48 39 46 08 41 8b d6 41 0f 94 c0 48 39 43 08 0f 94 c2 ....H......E..H9F.A..A...H9C....
33560 41 85 d0 0f 84 00 01 00 00 f6 46 20 80 75 11 48 8b ce ff 15 10 b5 01 00 85 c0 0f 88 b6 01 00 00 A.........F..u.H................
33580 f6 43 20 80 75 11 48 8b cb ff 15 f9 b4 01 00 85 c0 0f 88 9f 01 00 00 4c 8b 56 10 4c 3b 53 10 0f .C..u.H................L.V.L;S..
335a0 85 b0 01 00 00 48 8b 46 18 48 8b 4b 18 48 3b c1 74 10 48 83 f8 ff 74 0a 48 83 f9 ff 0f 85 93 01 .....H.F.H.K.H;.t.H...t.H.......
335c0 00 00 8b 4e 20 44 8b c1 8b 53 20 8b c2 41 c1 e8 02 c1 e8 02 41 83 e0 07 83 e0 07 44 3b c0 0f 85 ...N.D...S...A......A......D;...
335e0 71 01 00 00 b8 48 00 00 00 f6 c1 20 74 10 f6 c1 40 b9 30 00 00 00 0f 44 c8 48 03 ce eb 04 48 8b q....H......t...@.0....D.H....H.
33600 4e 48 f6 c2 20 74 11 f6 c2 40 ba 30 00 00 00 48 0f 44 d0 48 03 d3 eb 04 48 8b 53 48 41 83 f8 01 NH...t...@.0...H.D.H....H.SHA...
33620 75 09 0f b6 01 44 0f b6 0a eb 14 41 83 f8 02 75 09 0f b7 01 44 0f b7 0a eb 05 8b 01 44 8b 0a 41 u....D.....A...u....D.......D..A
33640 3b c1 0f 85 0d 01 00 00 49 83 fa 01 0f 84 ad 00 00 00 4d 0f af c2 e8 4c a9 01 00 85 c0 41 8b fe ;.......I.........M....L.....A..
33660 40 0f 94 c7 e9 90 00 00 00 48 8b 0d d8 b4 01 00 41 8b c6 48 3b f1 0f 94 c0 85 c2 0f 85 d4 00 00 @........H......A..H;...........
33680 00 48 3b d9 41 8b c6 0f 94 c0 41 85 c0 0f 85 c2 00 00 00 41 b8 02 00 00 00 48 8b d3 48 8b ce ff .H;.A.....A........A.....H..H...
336a0 15 cb b3 01 00 48 8b d8 48 85 c0 0f 84 85 00 00 00 48 3b 05 58 b2 01 00 41 8b fe 41 8b d6 41 8b .....H..H........H;.X...A..A..A.
336c0 ce 40 0f 94 c7 48 3b 05 8c b3 01 00 0f 94 c2 48 3b 05 72 b4 01 00 0f 94 c1 0b d1 0b d7 75 0b 48 .@...H;........H;.r..........u.H
336e0 8b c8 ff 15 d8 b1 01 00 8b f8 48 83 2b 01 75 09 48 8b cb ff 15 0f b3 01 00 85 ff 78 39 74 56 48 ..........H.+.u.H..........x9tVH
33700 8b 05 42 44 07 00 48 8b 48 18 48 39 0d 67 46 07 00 0f 85 fc 02 00 00 48 8b 05 da 4a 07 00 48 85 ..BD..H.H.H9.gF........H...J..H.
33720 c0 0f 84 de 02 00 00 48 ff 00 4c 8b 25 c7 4a 07 00 e9 fa 02 00 00 48 8b 3d 1b 38 02 00 bb 3c 0e .......H..L.%.J.......H.=.8...<.
33740 00 00 be 9e 44 00 00 4d 8b e6 4d 8b ee 49 8b ee e9 92 16 00 00 48 8b 05 ec 43 07 00 48 8b 48 18 ....D..M..M..I.......H...C..H.H.
33760 48 39 0d 19 4c 07 00 75 26 48 8b 05 00 40 07 00 48 85 c0 74 0c 48 ff 00 4c 8b 25 f1 3f 07 00 eb H9..L..u&H...@..H..t.H..L.%.?...
33780 2b 48 8b 0d d0 31 07 00 e8 53 c2 fd ff eb 1a 48 8b 0d c2 31 07 00 4c 8d 05 d3 3f 07 00 48 8d 15 +H...1...S.....H...1..L...?..H..
337a0 dc 4b 07 00 e8 47 b1 fd ff 4c 8b e0 4d 85 e4 75 1c 48 8b 3d a0 37 02 00 bb 3f 0e 00 00 be 0f 45 .K...G...L..M..u.H.=.7...?.....E
337c0 00 00 4d 8b ee 49 8b ee e9 1a 16 00 00 49 8b 44 24 08 49 8b cc 48 8b 15 94 35 07 00 4c 8b 80 90 ..M..I.......I.D$.I..H...5..L...
337e0 00 00 00 4d 85 c0 74 05 41 ff d0 eb 06 ff 15 85 b3 01 00 48 8b e8 48 85 c0 75 1c 48 8b 3d 56 37 ...M..t.A..........H..H..u.H.=V7
33800 02 00 bb 3f 0e 00 00 be 11 45 00 00 4d 8b ee 49 8b ee e9 d0 15 00 00 49 83 2c 24 01 75 09 49 8b ...?.....E..M..I.......I.,$.u.I.
33820 cc ff 15 e1 b1 01 00 4d 8b e6 4d 85 ed 75 30 48 8b 0d 7a b3 01 00 4c 8d 05 17 e5 06 00 48 8d 15 .......M..M..u0H..z...L......H..
33840 34 e9 06 00 48 8b 09 ff 15 33 b2 01 00 bb 3f 0e 00 00 be 14 45 00 00 4d 8b ee e9 67 15 00 00 48 4...H....3....?.....E..M...g...H
33860 8b 8c 24 c0 00 00 00 ff 15 cb af 01 00 4c 8b e0 48 85 c0 75 12 bb 3f 0e 00 00 be 15 45 00 00 4d ..$..........L..H..u..?.....E..M
33880 8b ee e9 3f 15 00 00 45 33 c0 49 8b d4 49 8b cd ff 15 da b1 01 00 4c 8b e8 48 85 c0 75 0f bb 3f ...?...E3.I..I........L..H..u..?
338a0 0e 00 00 be 17 45 00 00 e9 19 15 00 00 49 83 2c 24 01 75 09 49 8b cc ff 15 4b b1 01 00 48 8b 05 .....E.......I.,$.u.I....K...H..
338c0 74 b1 01 00 49 8b de 48 39 45 08 75 35 48 8b 5d 18 48 85 db 74 2c 48 8b 7d 10 48 8b cd 48 ff 03 t...I..H9E.u5H.].H..t,H.}.H..H..
338e0 48 8b ef 48 ff 07 48 83 29 01 75 06 ff 15 16 b1 01 00 4d 8b c5 48 8b d3 48 8b cf e8 90 b2 fd ff H..H..H.).u.......M..H..H.......
33900 eb 0b 49 8b d5 48 8b cd e8 b3 b3 fd ff 48 89 44 24 50 48 8b f8 48 85 db 74 0f 48 83 2b 01 75 09 ..I..H.......H.D$PH..H..t.H.+.u.
33920 48 8b cb ff 15 df b0 01 00 49 83 6d 00 01 4d 8b e6 75 09 49 8b cd ff 15 cc b0 01 00 4d 8b ee 48 H........I.m..M..u.I........M..H
33940 85 ff 75 0f bb 3f 0e 00 00 be 26 45 00 00 e9 73 14 00 00 48 83 6d 00 01 75 09 48 8b cd ff 15 a5 ..u..?....&E...s...H.m..u.H.....
33960 b0 01 00 48 8b 6c 24 50 41 8b de 48 3b 2d 9e af 01 00 41 8b ce 41 8b c6 0f 94 c3 48 3b 2d d6 b0 ...H.l$PA..H;-....A..A.....H;-..
33980 01 00 0f 94 c1 48 3b 2d bc b1 01 00 0f 94 c0 0b c8 0b cb 75 0b 48 8b cd ff 15 22 af 01 00 8b d8 .....H;-...........u.H....".....
339a0 85 db 79 16 48 8b 3d ad 35 02 00 bb 3f 0e 00 00 be 29 45 00 00 e9 2d 14 00 00 48 83 6d 00 01 75 ..y.H.=.5...?....)E...-...H.m..u
339c0 09 48 8b cd ff 15 3e b0 01 00 41 8b ce 85 db 0f 94 c1 e8 89 4d fd ff 48 85 c0 75 19 48 8b 3d 75 .H....>...A.........M..H..u.H.=u
339e0 35 02 00 bb 3f 0e 00 00 be 2b 45 00 00 48 8b e8 e9 f2 13 00 00 4c 8b c0 48 89 84 24 b8 00 00 00 5...?....+E..H.......L..H..$....
33a00 e9 5c 05 00 00 48 8b 0d 4c 2f 07 00 e8 cf bf fd ff eb 1a 48 8b 0d 3e 2f 07 00 4c 8d 05 d7 47 07 .\...H..L/.........H..>/..L...G.
33a20 00 48 8d 15 50 43 07 00 e8 c3 ae fd ff 4c 8b e0 4d 85 e4 75 1c 48 8b 3d 1c 35 02 00 bb 3d 0e 00 .H..PC.......L..M..u.H.=.5...=..
33a40 00 be a8 44 00 00 4d 8b ee 49 8b ee e9 96 13 00 00 49 8b 44 24 08 49 8b cc 48 8b 15 f0 3a 07 00 ...D..M..I.......I.D$.I..H...:..
33a60 4c 8b 80 90 00 00 00 4d 85 c0 74 05 41 ff d0 eb 06 ff 15 01 b1 01 00 4c 8b e8 48 85 c0 75 19 48 L......M..t.A..........L..H..u.H
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346c0 4d 0f af c1 e8 de 98 01 00 85 c0 41 8b fe 40 0f 94 c7 e9 90 00 00 00 48 8b 0d 6a a4 01 00 41 8b M..........A..@........H..j...A.
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348a0 45 08 48 8b cd 48 8b 15 a4 28 07 00 4c 8b 80 90 00 00 00 4d 85 c0 74 05 41 ff d0 eb 06 ff 15 b5 E.H..H...(..L......M..t.A.......
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34920 15 5b a1 01 00 bb 4f 0e 00 00 be f3 45 00 00 4d 8b e6 4d 8b ee e9 8c 04 00 00 48 8b 05 f7 a0 01 .[....O.....E..M..M.......H.....
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362a0 00 4d 85 c0 74 05 41 ff d0 eb 06 ff 15 c7 88 01 00 4c 8b e0 48 85 c0 75 0a bd 6b 3f 00 00 e9 d8 .M..t.A..........L..H..u..k?....
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36580 45 33 e4 49 83 2e 01 0f 85 65 01 00 00 49 8b ce e9 57 01 00 00 48 8b 15 3c 87 01 00 48 3b ca 74 E3.I.....e...I...W...H..<...H;.t
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365c0 00 75 7b 48 8b 94 24 90 00 00 00 44 8d 57 02 48 89 94 24 28 01 00 00 48 8d 94 24 20 01 00 00 8b .u{H..$....D.W.H..$(...H..$.....
365e0 c7 48 c1 e0 03 48 2b d0 4c 89 a4 24 18 01 00 00 4c 89 b4 24 20 01 00 00 4d 8b 58 08 f6 c1 20 74 .H...H+.L..$....L..$....M.X....t
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36640 4f 02 ff 15 f0 84 01 00 48 89 84 24 80 00 00 00 48 85 c0 75 07 bd ba 3f 00 00 eb 3f 4d 85 e4 74 O.......H..$....H..u...?...?M..t
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36680 01 48 89 4c f8 20 48 8b cb e8 f2 8c fd ff 48 8b f0 48 85 c0 75 48 bd c5 3f 00 00 33 ff bb 2e 0d .H.L..H.......H..H..uH..?..3....
366a0 00 00 48 8b 35 af 08 02 00 48 8b 8c 24 a0 00 00 00 48 83 29 01 75 06 ff 15 4b 83 01 00 4d 85 f6 ..H.5....H..$....H.).u...K...M..
366c0 0f 84 d0 00 00 00 49 83 2e 01 0f 85 c6 00 00 00 49 8b ce ff 15 2f 83 01 00 e9 b8 00 00 00 48 8b ......I.........I..../........H.
366e0 8c 24 80 00 00 00 48 83 29 01 75 06 ff 15 16 83 01 00 48 83 2b 01 75 09 48 8b cb ff 15 07 83 01 .$....H.).u.......H.+.u.H.......
36700 00 48 8b 05 30 83 01 00 33 db 49 39 47 08 75 35 49 8b 5f 18 48 85 db 74 2c 49 8b 7f 10 49 8b cf .H..0...3.I9G.u5I._.H..t,I...I..
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36760 cb ff 15 a1 82 01 00 48 83 2e 01 75 09 48 8b ce ff 15 92 82 01 00 48 85 ff 75 3c 33 c9 bd d7 3f .......H...u.H........H..u<3...?
36780 00 00 48 89 8c 24 80 00 00 00 bb 2e 0d 00 00 48 8b 35 c2 07 02 00 4d 85 ff 0f 84 6f 01 00 00 49 ..H..$.........H.5....M....o...I
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367e0 01 00 00 48 83 2f 01 75 09 48 8b cf ff 15 16 82 01 00 85 db 74 68 48 8b 15 fb 14 07 00 45 33 c0 ...H./.u.H..........thH......E3.
36800 48 8b 0d d9 17 07 00 e8 74 8b fd ff 48 8b d8 48 85 c0 75 18 48 8b 35 3d 07 02 00 bb 2f 0d 00 00 H.......t...H..H..u.H.5=..../...
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36840 ff 15 c2 81 01 00 48 8b 35 0b 07 02 00 bb 2f 0d 00 00 bd e9 3f 00 00 33 ff e9 cc 00 00 00 48 8b ......H.5...../.....?..3......H.
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385e0 4d 85 f6 74 05 49 ff 06 eb 1b ff 15 38 66 01 00 48 85 c0 74 05 45 33 f6 eb 0b 48 8b cb e8 de 73 M..t.I......8f..H..t.E3...H....s
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386c0 48 3b 0d b1 65 01 00 75 76 8b c6 48 8d 55 a0 48 c1 e0 03 44 8d 46 02 48 2b d0 4c 89 75 98 49 8b H;..e..uv..H.U.H...D.F.H+.L.u.I.
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425c0 48 89 8d 78 02 00 00 48 89 8d 80 02 00 00 48 89 8d 88 02 00 00 48 89 8d 90 02 00 00 48 89 8d 98 H..x...H......H......H......H...
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42b60 48 8b 05 d1 be 00 00 48 39 41 08 75 3d 48 8b 59 18 48 85 db 74 34 48 8b 41 10 48 ff 03 48 ff 00 H......H9A.u=H.Y.H..t4H.A.H..H..
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42c60 00 00 48 8b 15 f7 55 06 00 49 8b cd 48 89 7c 24 68 4c 8b e7 bb c5 02 00 00 e8 b2 b4 fc ff 85 c0 ..H...U..I..H.|$hL..............
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42cc0 00 00 41 be 15 1c 00 00 e9 ed 01 00 00 48 8b 44 24 50 48 8b 4d 58 48 ff 00 48 8b 49 08 48 8b 5c ..A..........H.D$PH.MXH..H.I.H.\
42ce0 24 50 48 89 5d c0 48 8b 41 08 48 3b 05 ff ba 00 00 75 0d 4c 8b 7d d0 48 ff 01 4d 8b 7f 08 eb 38 $PH.].H.A.H;.....u.L.}.H..M....8
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42d20 ff 92 88 00 00 00 eb 0d 48 8b 15 b1 50 06 00 ff 15 bb bc 00 00 4c 8b f8 4d 85 ff 75 10 bb c8 02 ........H...P........L..M..u....
42d40 00 00 41 be 24 1c 00 00 e9 8e 00 00 00 48 8b 0d cc 42 06 00 49 8b d7 ff 15 5b be 00 00 4c 8b e0 ..A.$........H...B..I....[...L..
42d60 48 85 c0 75 08 41 be 2e 1c 00 00 eb 69 49 83 2f 01 75 09 49 8b cf ff 15 8c bc 00 00 48 8b 0d 5d H..u.A......iI./.u.I........H..]
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42e00 85 e4 74 10 49 83 2c 24 01 75 09 49 8b cc ff 15 f4 bb 00 00 49 8b 85 90 00 00 00 4c 8d 4d 30 4c ..t.I.,$.u.I........I......L.M0L
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42e80 84 bb 00 00 4c 8b 4d d0 4d 8b c4 49 8b d7 49 8b cd e8 1a b5 fc ff 4c 8b 4d 30 49 8b cd 4c 8b 45 ....L.M.M..I..I.......L.M0I..L.E
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42f60 00 48 89 44 24 68 48 8b d0 48 85 c0 75 13 bb c9 02 00 00 41 be 86 1c 00 00 4c 8b e7 e9 27 57 00 .H.D$hH..H..u......A.....L...'W.
42f80 00 48 3b 15 88 b9 00 00 8b df 8b cf 8b c7 0f 94 c3 48 3b 15 b0 bb 00 00 0f 94 c1 48 3b 15 b6 ba .H;..............H;........H;...
42fa0 00 00 0f 94 c0 0b c8 0b cb 75 10 48 8b ca ff 15 0c b9 00 00 48 8b 54 24 68 8b d8 85 db 79 13 bb .........u.H........H.T$h....y..
42fc0 c9 02 00 00 41 be 87 1c 00 00 4c 8b e7 e9 d6 56 00 00 48 83 2a 01 75 09 48 8b ca ff 15 27 ba 00 ....A.....L....V..H.*.u.H....'..
42fe0 00 48 89 7c 24 68 85 db 0f 84 95 06 00 00 48 8b 05 53 4b 06 00 48 8b 48 18 48 39 0d 30 48 06 00 .H.|$h........H..SK..H.H.H9.0H..
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43020 00 e8 ba c9 fc ff eb 1a 48 8b 0d 29 39 06 00 4c 8d 05 d2 48 06 00 48 8d 15 f3 47 06 00 e8 ae b8 ........H..)9..L...H..H...G.....
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43080 d0 eb 0b 48 8b 4c 24 50 ff 15 ea ba 00 00 48 89 44 24 58 48 85 c0 75 13 bb c9 02 00 00 41 be 90 ...H.L$P......H.D$XH..u......A..
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43120 9c bb fc ff 48 8b 4c 24 50 48 89 44 24 68 48 85 c9 74 0c 48 83 29 01 75 06 ff 15 c9 b8 00 00 48 ....H.L$PH.D$hH..t.H.).u.......H
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43160 4c 24 58 48 83 29 01 75 06 ff 15 99 b8 00 00 48 8b 15 42 48 06 00 45 33 c9 48 8b 4c 24 68 45 33 L$XH.).u.......H..BH..E3.H.L$hE3
43180 c0 e8 fa ac fc ff 48 89 44 24 58 48 85 c0 75 13 bb c9 02 00 00 41 be a2 1c 00 00 4c 8b e7 e9 05 ......H.D$XH..u......A.....L....
431a0 55 00 00 48 8b 4c 24 68 48 83 29 01 75 06 ff 15 54 b8 00 00 48 8b 54 24 58 8b df 48 3b 15 4e b7 U..H.L$hH.).u...T...H.T$X..H;.N.
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44340 44 24 50 48 ff 00 48 8b 4c 24 68 48 83 29 01 75 06 ff 15 b1 a6 00 00 48 8b 44 24 50 48 8b ce 48 D$PH..H.L$hH.).u.......H.D$PH..H
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443c0 4c 8b e7 e9 e0 42 00 00 48 8b 5c 24 50 48 89 5c 24 68 48 ff 03 48 8b 4c 24 50 48 83 29 01 75 06 L....B..H.\$PH.\$hH..H.L$PH.).u.
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44400 a6 00 00 4c 3b 3d 3e a7 00 00 48 89 7c 24 68 74 2c 48 8b 15 d8 3e 06 00 49 8b cf e8 70 95 fc ff ...L;=>...H.|$ht,H...>..I...p...
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44480 ef 4c 8b e7 e9 1f 42 00 00 48 8b 15 f8 3b 06 00 45 33 c9 48 8b c8 45 8d 41 01 e8 e1 99 fc ff 48 .L....B..H...;..E3.H..E.A......H
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44580 00 48 8b 4c 24 50 45 33 c9 45 33 c0 33 d2 e8 3d ac fc ff 48 8b 4c 24 50 48 83 29 01 75 06 ff 15 .H.L$PE3.E3.3..=...H.L$PH.).u...
445a0 64 a4 00 00 48 89 7c 24 50 bb df 02 00 00 41 be 4d 1e 00 00 4c 8b ff 4c 8b ef 4c 8b e7 e9 e6 40 d...H.|$P.....A.M...L..L..L....@
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445e0 06 ff 15 91 a5 00 00 48 89 44 24 50 48 85 c0 75 19 bb e0 02 00 00 41 be 5f 1e 00 00 4c 8b ff 4c .......H.D$PH..u......A._...L..L
44600 8b ef 4c 8b e7 e9 9e 40 00 00 48 8b 55 a8 41 b8 03 00 00 00 48 8b c8 ff 15 53 a4 00 00 48 89 44 ..L....@..H.U.A.....H....S...H.D
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447c0 3e 00 00 48 8b 15 ae 26 06 00 48 8b 4c 24 50 e8 7c b2 fc ff 48 89 44 24 70 48 85 c0 75 19 bb e3 >..H...&..H.L$P.|...H.D$pH..u...
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44880 4c 24 70 e8 08 a3 fc ff eb 0a 48 8b 54 24 50 e8 2c a4 fc ff 48 8b ce 48 89 44 24 68 e8 ff 95 00 L$p.......H.T$P.,...H..H.D$h....
448a0 00 48 8b 4c 24 50 4c 8b ef e8 22 96 00 00 48 89 7c 24 50 48 39 7c 24 68 75 16 bb e3 02 00 00 41 .H.L$PL..."...H.|$PH9|$hu......A
448c0 be a1 1e 00 00 4c 8b ff 4c 8b e7 e9 d8 3d 00 00 48 8b 4c 24 70 e8 f6 95 00 00 48 8b 4c 24 68 48 .....L..L....=..H.L$p.....H.L$hH
448e0 89 7c 24 70 e8 97 41 fc ff 8b d8 85 c0 79 16 bb e3 02 00 00 41 be a4 1e 00 00 4c 8b ff 4c 8b e7 .|$p..A......y......A.....L..L..
44900 e9 a3 3d 00 00 48 8b 4c 24 68 e8 c1 95 00 00 48 89 7c 24 68 85 db 74 6b 48 8b 15 e1 33 06 00 45 ..=..H.L$h.....H.|$h..tkH...3..E
44920 33 c0 48 8b 0d b7 36 06 00 e8 52 aa fc ff 48 89 44 24 68 48 85 c0 75 16 bb e4 02 00 00 41 be af 3.H...6...R...H.D$hH..u......A..
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44980 3d 00 00 48 8b 05 be 31 06 00 48 8b 48 18 48 39 0d 93 33 06 00 75 28 48 8b 0d a2 2e 06 00 48 85 =..H...1..H.H.H9..3..u(H......H.
449a0 c9 74 0e e8 48 95 00 00 48 8b 05 91 2e 06 00 eb 28 48 8b 0d a0 1f 06 00 e8 23 b0 fc ff eb 1a 48 .t..H...H.......(H.......#.....H
449c0 8b 0d 92 1f 06 00 4c 8d 05 73 2e 06 00 48 8d 15 54 33 06 00 e8 17 9f fc ff 48 89 44 24 70 48 85 ......L..s...H..T3.......H.D$pH.
449e0 c0 75 16 bb e5 02 00 00 41 be c5 1e 00 00 4c 8b ff 4c 8b e7 e9 af 3c 00 00 48 8b 15 30 26 06 00 .u......A.....L..L....<..H..0&..
44a00 48 8b c8 e8 48 b0 fc ff 48 89 44 24 50 48 85 c0 75 16 bb e5 02 00 00 41 be c7 1e 00 00 4c 8b ff H...H...H.D$PH..u......A.....L..
44a20 4c 8b e7 e9 80 3c 00 00 48 8b 4c 24 70 e8 9e 94 00 00 48 8b 15 9f 27 06 00 48 8b 4c 24 50 e8 0d L....<..H.L$p.....H...'..H.L$P..
44a40 b0 fc ff 48 89 44 24 70 48 85 c0 75 16 bb e5 02 00 00 41 be ca 1e 00 00 4c 8b ff 4c 8b e7 e9 45 ...H.D$pH..u......A.....L..L...E
44a60 3c 00 00 48 8b 4c 24 50 e8 63 94 00 00 48 8b 15 44 2f 06 00 45 33 c0 49 8b cf ff 15 f0 9f 00 00 <..H.L$P.c...H..D/..E3.I........
44a80 48 89 44 24 50 48 85 c0 75 16 bb e5 02 00 00 41 be cd 1e 00 00 4c 8b ff 4c 8b e7 e9 08 3c 00 00 H.D$PH..u......A.....L..L....<..
44aa0 48 8b 15 91 9f 00 00 48 8b f7 48 8b 4c 24 70 e8 6c 94 00 00 48 8b 4c 24 70 85 c0 74 40 48 8b 71 H......H..H.L$p.l...H.L$p..t@H.q
44ac0 18 48 85 f6 74 37 48 8b 59 10 48 8b ce e8 1e 94 00 00 48 8b cb e8 16 94 00 00 48 8b 4c 24 70 48 .H..t7H.Y.H.......H.......H.L$pH
44ae0 89 5c 24 70 e8 e7 93 00 00 4c 8b 44 24 50 48 8b d6 48 8b 4c 24 70 e8 95 a0 fc ff eb 0a 48 8b 54 .\$p.....L.D$PH..H.L$p.......H.T
44b00 24 50 e8 b9 a1 fc ff 48 8b ce 48 89 44 24 68 e8 8c 93 00 00 48 8b 4c 24 50 e8 b2 93 00 00 48 89 $P.....H..H.D$h.....H.L$P.....H.
44b20 7c 24 50 48 39 7c 24 68 75 16 bb e5 02 00 00 41 be db 1e 00 00 4c 8b ff 4c 8b e7 e9 68 3b 00 00 |$PH9|$hu......A.....L..L...h;..
44b40 48 8b 4c 24 70 e8 86 93 00 00 48 8b 4c 24 68 48 89 7c 24 70 e8 27 3f fc ff 8b d8 85 c0 79 16 bb H.L$p.....H.L$hH.|$p.'?......y..
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44ba0 c0 75 16 bb e6 02 00 00 41 be e9 1e 00 00 4c 8b ff 4c 8b e7 e9 ef 3a 00 00 45 33 c9 45 33 c0 33 .u......A.....L..L....:..E3.E3.3
44bc0 d2 48 8b c8 e8 07 a6 fc ff 48 8b 4c 24 68 e8 fd 92 00 00 48 89 7c 24 68 bb e6 02 00 00 41 be ed .H.......H.L$h.....H.|$h.....A..
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44c00 ff 15 ea 9e 00 00 48 89 44 24 68 48 85 c0 75 16 bb e7 02 00 00 41 be ff 1e 00 00 4c 8b ff 4c 8b ......H.D$hH..u......A.....L..L.
44c20 e7 e9 82 3a 00 00 48 8b 55 d8 41 b8 04 00 00 00 48 8b c8 ff 15 37 9e 00 00 48 89 44 24 70 48 85 ...:..H.U.A.....H....7...H.D$pH.
44c40 c0 75 16 bb e7 02 00 00 41 be 01 1f 00 00 4c 8b ff 4c 8b e7 e9 4f 3a 00 00 48 8b 4c 24 68 e8 6d .u......A.....L..L...O:..H.L$h.m
44c60 92 00 00 48 8b 4c 24 70 48 89 7c 24 68 e8 0e 3e fc ff 8b d8 85 c0 79 16 bb e7 02 00 00 41 be 03 ...H.L$pH.|$h..>......y......A..
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44ca0 2d 06 00 45 33 c0 48 8b 0d 33 33 06 00 e8 ce a6 fc ff 48 89 44 24 70 48 85 c0 75 16 bb e8 02 00 -..E3.H..33.......H.D$pH..u.....
44cc0 00 41 be 0e 1f 00 00 4c 8b ff 4c 8b e7 e9 d6 39 00 00 45 33 c9 45 33 c0 33 d2 48 8b c8 e8 ee a4 .A.....L..L....9..E3.E3.3.H.....
44ce0 fc ff 48 8b 4c 24 70 e8 e4 91 00 00 48 89 7c 24 70 bb e8 02 00 00 41 be 12 1f 00 00 4c 8b ff 4c ..H.L$p.....H.|$p.....A.....L..L
44d00 8b e7 e9 a1 39 00 00 48 8b 05 3a 9e 00 00 4c 8b 75 50 4c 8b 65 c0 48 8b 75 90 8b cf 48 3b f0 0f ....9..H..:...L.uPL.e.H.u...H;..
44d20 94 c1 e8 39 3a fc ff 48 89 44 24 70 48 85 c0 75 19 bb ec 02 00 00 41 be 2e 1f 00 00 4c 8b ff 4c ...9:..H.D$pH..u......A.....L..L
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44d60 ed 02 00 00 41 be 3a 1f 00 00 4c 8b ff 4c 8b ef 4c 8b e7 e9 30 39 00 00 0f 85 8e 02 00 00 48 8b ....A.:...L..L..L...09........H.
44d80 ce e8 6a 91 00 00 48 8b 05 bb 2d 06 00 48 89 75 b0 48 8b 48 18 48 39 0d f4 2d 06 00 75 28 48 8b ..j...H...-..H.u.H.H.H9..-..u(H.
44da0 0d f3 31 06 00 48 85 c9 74 0e e8 41 91 00 00 48 8b 05 e2 31 06 00 eb 28 48 8b 0d 99 1b 06 00 e8 ..1..H..t..A...H...1...(H.......
44dc0 1c ac fc ff eb 1a 48 8b 0d 8b 1b 06 00 4c 8d 05 c4 31 06 00 48 8d 15 b5 2d 06 00 e8 10 9b fc ff ......H......L...1..H...-.......
44de0 48 89 44 24 70 48 85 c0 75 19 bb ef 02 00 00 41 be 4f 1f 00 00 4c 8b ff 4c 8b ef 4c 8b e7 e9 a5 H.D$pH..u......A.O...L..L..L....
44e00 38 00 00 48 8b 15 36 1b 06 00 48 8b c8 e8 3e ac fc ff 48 89 44 24 68 48 85 c0 75 19 bb ef 02 00 8..H..6...H...>...H.D$hH..u.....
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44e40 01 00 00 00 ff 15 ee 9c 00 00 48 89 44 24 70 48 85 c0 75 19 bb ef 02 00 00 41 be 54 1f 00 00 4c ..........H.D$pH..u......A.T...L
44e60 8b ff 4c 8b ef 4c 8b e7 e9 3b 38 00 00 48 8b ce e8 7b 90 00 00 48 8b 44 24 70 48 89 70 18 ff 15 ..L..L...;8..H...{...H.D$pH.p...
44e80 64 99 00 00 48 89 44 24 50 48 85 c0 75 19 bb ef 02 00 00 41 be 59 1f 00 00 4c 8b ff 4c 8b ef 4c d...H.D$PH..u......A.Y...L..L..L
44ea0 8b e7 e9 01 38 00 00 48 8b 05 9a 2c 06 00 48 8b 48 18 48 39 0d f7 2d 06 00 75 28 48 8b 0d 2e 28 ....8..H...,..H.H.H9..-..u(H...(
44ec0 06 00 48 85 c9 74 0e e8 24 90 00 00 4c 8b 2d 1d 28 06 00 eb 2b 48 8b 0d 7c 1a 06 00 e8 ff aa fc ..H..t..$...L.-.(...+H..|.......
44ee0 ff eb 1a 48 8b 0d 6e 1a 06 00 4c 8d 05 ff 27 06 00 48 8d 15 b8 2d 06 00 e8 f3 99 fc ff 4c 8b e8 ...H..n...L...'..H...-.......L..
44f00 4d 85 ed 75 16 bb ef 02 00 00 41 be 5b 1f 00 00 4c 8b ff 4c 8b e7 e9 8d 37 00 00 48 8b 15 56 1c M..u......A.[...L..L....7..H..V.
44f20 06 00 49 8b cd e8 26 ab fc ff 48 89 44 24 58 48 85 c0 75 16 bb ef 02 00 00 41 be 5d 1f 00 00 4c ..I...&...H.D$XH..u......A.]...L
44f40 8b ff 4c 8b e7 e9 5e 37 00 00 49 8b cd e8 7e 8f 00 00 4c 8b 44 24 58 4c 8b ef 48 8b 15 1f 19 06 ..L...^7..I...~...L.D$XL..H.....
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44fa0 dc a3 fc ff 48 89 44 24 58 48 85 c0 75 16 bb ef 02 00 00 41 be 62 1f 00 00 4c 8b ff 4c 8b e7 e9 ....H.D$XH..u......A.b...L..L...
44fc0 e4 36 00 00 48 8b 4c 24 68 e8 02 8f 00 00 48 8b 4c 24 70 48 89 7c 24 68 e8 f3 8e 00 00 48 8b 4c .6..H.L$h.....H.L$pH.|$h.....H.L
44fe0 24 50 48 89 7c 24 70 e8 e4 8e 00 00 48 8b 5c 24 58 48 8b ce 48 89 5d 90 48 89 7c 24 50 e8 ce 8e $PH.|$p.....H.\$XH..H.].H.|$P...
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45020 8b 0d 62 30 06 00 4c 89 6d b0 e8 c1 8e 00 00 48 8b 05 52 30 06 00 48 8b ce 48 89 45 90 e8 8e 8e ..b0..L.m......H..R0..H..H.E....
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45fe0 8b 15 22 15 06 00 49 8b cd e8 62 9a fc ff 48 89 44 24 70 48 85 c0 75 16 bb 0b 03 00 00 41 be 1e .."...I...b...H.D$pH..u......A..
46000 21 00 00 4c 8b ff 4c 8b e7 e9 9a 26 00 00 49 8b cd e8 ba 7e 00 00 4c 8b 44 24 70 4c 8b ef 48 8b !..L..L....&..I....~..L.D$pL..H.
46020 15 5b 08 06 00 48 8b 4c 24 68 ff 15 b0 87 00 00 85 c0 79 16 bb 0b 03 00 00 41 be 21 21 00 00 4c .[...H.L$h........y......A.!!..L
46040 8b ff 4c 8b e7 e9 5e 26 00 00 48 8b 4c 24 70 e8 7c 7e 00 00 4c 8b 44 24 68 48 8b 54 24 58 48 8b ..L...^&..H.L$p.|~..L.D$hH.T$XH.
46060 4c 24 50 e8 18 93 fc ff 48 89 44 24 70 48 85 c0 75 16 bb 0b 03 00 00 41 be 23 21 00 00 4c 8b ff L$P.....H.D$pH..u......A.#!..L..
46080 4c 8b e7 e9 20 26 00 00 48 8b 4c 24 50 e8 3e 7e 00 00 48 8b 4c 24 58 48 89 7c 24 50 e8 2f 7e 00 L....&..H.L$P.>~..H.L$XH.|$P./~.
460a0 00 48 8b 4c 24 68 48 89 7c 24 58 e8 20 7e 00 00 48 8b 44 24 70 48 8b 15 a4 09 06 00 48 8b c8 48 .H.L$hH.|$X..~..H.D$pH......H..H
460c0 89 45 48 48 89 7c 24 70 e8 83 99 fc ff 48 89 44 24 68 48 85 c0 75 16 bb 0c 03 00 00 41 be 32 21 .EHH.|$p.....H.D$hH..u......A.2!
460e0 00 00 4c 8b ff 4c 8b e7 e9 bb 25 00 00 48 8b 15 44 89 00 00 48 8b c8 e8 24 7e 00 00 48 8b 4c 24 ..L..L....%..H..D...H...$~..H.L$
46100 68 85 c0 74 36 48 8b 51 18 48 89 54 24 58 48 85 d2 74 39 48 8b 59 10 48 8b ca e8 d1 7d 00 00 48 h..t6H.Q.H.T$XH..t9H.Y.H....}..H
46120 8b cb e8 c9 7d 00 00 48 8b 4c 24 68 48 89 5c 24 68 e8 9a 7d 00 00 48 8b 4c 24 68 48 8b 54 24 58 ....}..H.L$hH.\$h..}..H.L$hH.T$X
46140 48 85 d2 74 07 e8 76 8b fc ff eb 05 e8 6f 8d fc ff 48 8b 4c 24 58 48 89 44 24 70 e8 40 7d 00 00 H..t..v......o...H.L$XH.D$p.@}..
46160 48 89 7c 24 58 48 39 7c 24 70 75 16 bb 0c 03 00 00 41 be 40 21 00 00 4c 8b ff 4c 8b e7 e9 26 25 H.|$XH9|$pu......A.@!..L..L...&%
46180 00 00 48 8b 4c 24 68 e8 44 7d 00 00 48 8b 44 24 70 45 33 c0 48 8b 4d 88 49 8b d6 48 89 45 18 48 ..H.L$h.D}..H.D$pE3.H.M.I..H.E.H
461a0 89 7c 24 68 ff 15 c6 88 00 00 48 89 44 24 70 48 85 c0 0f 84 b7 09 00 00 48 8b f7 0f 1f 44 00 00 .|$h......H.D$pH........H....D..
461c0 48 8b c8 e8 b8 28 fc ff 8b d8 85 c0 0f 88 2b 0d 00 00 48 8b 4c 24 70 e8 f4 7c 00 00 48 89 7c 24 H....(........+...H.L$p..|..H.|$
461e0 70 85 db 0f 84 02 0d 00 00 48 8b 15 d0 0b 06 00 49 8b cc e8 58 98 fc ff 48 89 44 24 68 48 85 c0 p........H......I...X...H.D$hH..
46200 0f 84 cf 0c 00 00 48 8b 55 88 49 8b ce ff 15 0d 88 00 00 48 89 44 24 58 48 85 c0 0f 84 9e 0c 00 ......H.U.I........H.D$XH.......
46220 00 b9 01 00 00 00 ff 15 0c 89 00 00 48 89 44 24 50 48 8b d8 48 85 c0 0f 84 6c 0c 00 00 48 8b 44 ............H.D$PH..H....l...H.D
46240 24 58 48 89 43 18 48 8b 15 eb 87 00 00 48 8b 4c 24 68 48 89 7c 24 58 e8 c4 7c 00 00 48 8b 4c 24 $XH.C.H......H.L$hH.|$X..|..H.L$
46260 68 85 c0 74 36 48 8b 51 18 48 89 54 24 58 48 85 d2 74 3e 48 8b 59 10 48 8b ca e8 71 7c 00 00 48 h..t6H.Q.H.T$XH..t>H.Y.H...q|..H
46280 8b cb e8 69 7c 00 00 48 8b 4c 24 68 48 89 5c 24 68 e8 3a 7c 00 00 48 8b 4c 24 68 48 8b 54 24 58 ...i|..H.L$hH.\$h.:|..H.L$hH.T$X
462a0 48 85 d2 74 0c 4c 8b 44 24 50 e8 e1 88 fc ff eb 0a 48 8b 54 24 50 e8 05 8a fc ff 48 8b 4c 24 58 H..t.L.D$P.......H.T$P.....H.L$X
462c0 48 89 44 24 70 e8 d6 7b 00 00 48 8b 4c 24 50 48 89 7c 24 58 e8 f7 7b 00 00 48 89 7c 24 50 48 39 H.D$p..{..H.L$PH.|$X..{..H.|$PH9
462e0 7c 24 70 0f 84 aa 0b 00 00 48 8b 4c 24 68 e8 dd 7b 00 00 48 8b 44 24 70 48 8b 4d 20 48 89 45 20 |$p......H.L$h..{..H.D$pH.M.H.E.
46300 48 89 7c 24 68 e8 96 7b 00 00 48 8b 15 a7 16 06 00 41 b8 04 00 00 00 48 8b 4d 88 ff 15 4f 87 00 H.|$h..{..H......A.....H.M...O..
46320 00 48 89 44 24 70 48 85 c0 0f 84 4e 0b 00 00 48 8b c8 e8 49 27 fc ff 8b d8 85 c0 0f 88 26 0b 00 .H.D$pH....N...H...I'........&..
46340 00 48 8b 4c 24 70 e8 85 7b 00 00 48 89 7c 24 70 85 db 74 68 48 8b 4d 18 b8 01 00 00 00 89 44 24 .H.L$p..{..H.|$p..thH.M.......D$
46360 40 45 33 c9 89 7c 24 38 45 33 c0 89 44 24 30 33 d2 48 8d 45 88 48 89 7c 24 28 48 89 44 24 20 e8 @E3..|$8E3..D$03.H.E.H.|$(H.D$..
46380 1c 82 fc ff 48 89 44 24 70 48 85 c0 0f 84 09 08 00 00 4c 8b 05 1f 16 06 00 48 8b d0 49 8b cf ff ....H.D$pH........L......H..I...
463a0 15 93 85 00 00 85 c0 0f 88 d8 07 00 00 48 8b 4c 24 70 e8 19 7b 00 00 48 89 7c 24 70 48 8b 05 85 .............H.L$p..{..H.|$pH...
463c0 17 06 00 48 8b 48 18 48 39 0d 0a 19 06 00 75 28 48 8b 0d c1 1f 06 00 48 85 c9 74 0e e8 0f 7b 00 ...H.H.H9.....u(H......H..t...{.
463e0 00 48 8b 05 b0 1f 06 00 eb 28 48 8b 0d 67 05 06 00 e8 ea 95 fc ff eb 1a 48 8b 0d 59 05 06 00 4c .H.......(H..g..........H..Y...L
46400 8d 05 92 1f 06 00 48 8d 15 cb 18 06 00 e8 de 84 fc ff 48 89 44 24 68 48 85 c0 0f 84 31 0a 00 00 ......H...........H.D$hH....1...
46420 48 8b 15 91 0a 06 00 48 8b c8 e8 21 96 fc ff 48 89 44 24 50 48 85 c0 0f 84 fe 09 00 00 48 8b 4c H......H...!...H.D$PH........H.L
46440 24 68 e8 89 7a 00 00 48 8b 15 ea 85 00 00 48 8b 4c 24 50 48 89 7c 24 68 e8 c3 7a 00 00 48 8b 4c $h..z..H......H.L$PH.|$h..z..H.L
46460 24 50 85 c0 74 36 48 8b 51 18 48 89 54 24 68 48 85 d2 74 3c 48 8b 59 10 48 8b ca e8 70 7a 00 00 $P..t6H.Q.H.T$hH..t<H.Y.H...pz..
46480 48 8b cb e8 68 7a 00 00 48 8b 4c 24 50 48 89 5c 24 50 e8 39 7a 00 00 48 8b 4c 24 50 48 8b 54 24 H...hz..H.L$PH.\$P.9z..H.L$PH.T$
464a0 68 48 85 d2 74 0a 4d 8b c7 e8 e2 86 fc ff eb 08 49 8b d7 e8 08 88 fc ff 48 8b 4c 24 68 48 89 44 hH..t.M.........I.......H.L$hH.D
464c0 24 70 e8 d9 79 00 00 48 89 7c 24 68 48 39 7c 24 70 0f 84 4e 09 00 00 48 8b 4c 24 50 e8 ef 79 00 $p..y..H.|$hH9|$p..N...H.L$P..y.
464e0 00 48 8b 5c 24 70 48 8b 4d 98 48 89 5d 98 48 89 7c 24 50 e8 a8 79 00 00 41 b9 01 00 00 00 89 7c .H.\$pH.M.H.].H.|$P..y..A......|
46500 24 20 45 33 c0 48 8b cb 49 8d 51 fe e8 4f 77 fc ff 48 89 44 24 70 48 85 c0 0f 84 f0 08 00 00 48 $.E3.H..I.Q..Ow..H.D$pH........H
46520 8b d0 48 8b cb ff 15 8d 87 00 00 48 89 44 24 50 48 85 c0 0f 84 c0 08 00 00 48 8b 4c 24 70 e8 8d ..H........H.D$PH........H.L$p..
46540 79 00 00 48 8b cb 48 89 7c 24 70 48 8b 5c 24 50 48 89 5d 98 e8 77 79 00 00 48 8b 15 68 04 06 00 y..H..H.|$pH.\$PH.]..wy..H..h...
46560 48 8b cb e8 e8 94 fc ff 48 89 44 24 50 48 85 c0 0f 84 6d 08 00 00 b9 01 00 00 00 ff 15 b7 85 00 H.......H.D$PH....m.............
46580 00 48 89 44 24 70 48 85 c0 0f 84 3e 08 00 00 48 8b 5d 20 48 8b cb e8 55 79 00 00 48 8b 44 24 70 .H.D$pH....>...H.].H...Uy..H.D$p
465a0 48 89 58 18 ff 15 3e 82 00 00 48 89 44 24 68 48 85 c0 0f 84 ff 07 00 00 4c 8b 05 41 05 06 00 48 H.X...>...H.D$hH........L..A...H
465c0 8b c8 48 8b 15 df 04 06 00 ff 15 11 82 00 00 85 c0 0f 88 ca 07 00 00 4c 8b 44 24 68 48 8b 54 24 ..H....................L.D$hH.T$
465e0 70 48 8b 4c 24 50 e8 95 8d fc ff 48 89 44 24 58 48 85 c0 0f 84 92 07 00 00 48 8b 4c 24 50 e8 cd pH.L$P.....H.D$XH........H.L$P..
46600 78 00 00 48 8b 4c 24 70 48 89 7c 24 50 e8 be 78 00 00 48 8b 4c 24 68 48 89 7c 24 70 e8 af 78 00 x..H.L$pH.|$P..x..H.L$hH.|$p..x.
46620 00 48 8b ce 48 89 7c 24 68 48 8b 74 24 58 48 89 75 e0 e8 69 78 00 00 48 8b 05 0a 15 06 00 48 89 .H..H.|$hH.t$XH.u..ix..H......H.
46640 7c 24 58 48 8b 48 18 48 39 0d fa 1c 06 00 75 28 48 8b 0d 09 12 06 00 48 85 c9 74 0e e8 8f 78 00 |$XH.H.H9.....u(H......H..t...x.
46660 00 48 8b 05 f8 11 06 00 eb 28 48 8b 0d e7 02 06 00 e8 6a 93 fc ff eb 1a 48 8b 0d d9 02 06 00 4c .H.......(H.......j.....H......L
46680 8d 05 da 11 06 00 48 8d 15 bb 1c 06 00 e8 5e 82 fc ff 48 89 44 24 58 48 85 c0 0f 84 d5 06 00 00 ......H.......^...H.D$XH........
466a0 48 8b 15 b1 0c 06 00 48 8b c8 e8 a1 93 fc ff 48 89 44 24 68 48 85 c0 0f 84 a2 06 00 00 48 8b 4c H......H.......H.D$hH........H.L
466c0 24 58 e8 09 78 00 00 b9 01 00 00 00 48 89 7c 24 58 ff 15 61 84 00 00 48 89 44 24 58 48 85 c0 0f $X..x.......H.|$X..a...H.D$XH...
466e0 84 64 06 00 00 48 8b ce e8 03 78 00 00 48 8b 44 24 58 48 89 70 18 ff 15 ec 80 00 00 48 89 44 24 .d...H....x..H.D$XH.p.......H.D$
46700 70 48 85 c0 0f 84 29 06 00 00 4c 8b 05 ff 81 00 00 48 8b c8 48 8b 15 95 01 06 00 ff 15 bf 80 00 pH....)...L......H..H...........
46720 00 85 c0 0f 88 f4 05 00 00 4c 8b 44 24 70 48 8b 54 24 58 48 8b 4c 24 68 e8 43 8c fc ff 48 89 44 .........L.D$pH.T$XH.L$h.C...H.D
46740 24 50 48 85 c0 0f 84 bc 05 00 00 48 8b 4c 24 68 e8 7b 77 00 00 48 8b 4c 24 58 48 89 7c 24 68 e8 $PH........H.L$h.{w..H.L$XH.|$h.
46760 6c 77 00 00 48 8b 4c 24 70 48 89 7c 24 58 e8 5d 77 00 00 48 8b 15 e6 82 00 00 48 8b 4c 24 50 48 lw..H.L$pH.|$X.]w..H......H.L$PH
46780 89 7c 24 70 e8 97 77 00 00 85 c0 0f 85 ad 00 00 00 48 8b 15 a8 80 00 00 48 8b 4c 24 50 e8 7e 77 .|$p..w..........H......H.L$P.~w
467a0 00 00 85 c0 0f 85 94 00 00 00 48 8b 4c 24 50 ff 15 03 83 00 00 48 89 44 24 68 48 85 c0 0f 84 3a ..........H.L$P......H.D$hH....:
467c0 04 00 00 48 8b 4c 24 50 e8 03 77 00 00 48 8b 4c 24 68 48 8b f7 48 89 7c 24 50 48 8b 41 08 48 8b ...H.L$P..w..H.L$hH..H.|$PH.A.H.
467e0 98 e0 00 00 00 ff d3 48 89 44 24 70 48 85 c0 0f 84 d2 03 00 00 48 8b 4c 24 68 be 01 00 00 00 ff .......H.D$pH........H.L$h......
46800 d3 48 89 44 24 58 48 85 c0 0f 84 b8 03 00 00 48 8b 4c 24 68 ff d3 48 8b c8 8d 56 01 e8 ef 6f fc .H.D$XH........H.L$h..H...V...o.
46820 ff 85 c0 0f 88 88 03 00 00 48 8b 4c 24 68 e8 9d 76 00 00 48 8b 75 e0 48 89 7c 24 68 eb 68 48 8b .........H.L$h..v..H.u.H.|$h.hH.
46840 5c 24 50 48 8b 4b 10 48 83 f9 02 0f 85 88 04 00 00 48 8b 15 08 82 00 00 48 8b cb e8 c0 76 00 00 \$PH.K.H.........H......H....v..
46860 48 8b 4b 18 85 c0 74 0b 48 89 4c 24 70 48 8b 43 20 eb 10 48 8b 09 48 89 4c 24 70 48 8b 43 18 48 H.K...t.H.L$pH.C...H..H.L$pH.C.H
46880 8b 40 08 48 89 44 24 58 e8 63 76 00 00 48 8b 4c 24 58 e8 59 76 00 00 48 8b 4c 24 50 e8 2f 76 00 .@.H.D$X.cv..H.L$X.Yv..H.L$P./v.
468a0 00 48 89 7c 24 50 48 8b 44 24 70 48 8b 4d 38 48 89 45 38 e8 e8 75 00 00 48 8b 5c 24 58 48 8b 4d .H.|$PH.D$pH.M8H.E8..u..H.\$XH.M
468c0 e8 48 89 5d e8 48 89 7c 24 70 e8 d1 75 00 00 48 8b 15 ba 05 06 00 48 8b cb 48 89 7c 24 58 e8 6d .H.].H.|$p..u..H......H..H.|$X.m
468e0 91 fc ff 48 89 44 24 58 48 85 c0 0f 84 d2 03 00 00 48 8b 15 40 81 00 00 48 8b c8 e8 20 76 00 00 ...H.D$XH........H..@...H....v..
46900 48 8b 4c 24 58 85 c0 74 36 48 8b 51 18 48 89 54 24 70 48 85 d2 74 39 48 8b 59 10 48 8b ca e8 cd H.L$X..t6H.Q.H.T$pH..t9H.Y.H....
46920 75 00 00 48 8b cb e8 c5 75 00 00 48 8b 4c 24 58 48 89 5c 24 58 e8 96 75 00 00 48 8b 4c 24 58 48 u..H....u..H.L$XH.\$X..u..H.L$XH
46940 8b 54 24 70 48 85 d2 74 07 e8 72 83 fc ff eb 05 e8 6b 85 fc ff 48 8b 4c 24 70 48 89 44 24 50 e8 .T$pH..t..r......k...H.L$pH.D$P.
46960 3c 75 00 00 48 89 7c 24 70 48 39 7c 24 50 0f 84 39 03 00 00 48 8b 4c 24 58 e8 52 75 00 00 48 8b <u..H.|$pH9|$P..9...H.L$X.Ru..H.
46980 4c 24 50 48 89 7c 24 58 e8 43 75 00 00 48 8b 15 44 02 06 00 48 8b ce 48 89 7c 24 50 e8 af 90 fc L$PH.|$X.Cu..H..D...H..H.|$P....
469a0 ff 48 89 44 24 58 48 85 c0 0f 84 e8 02 00 00 48 8b 15 82 80 00 00 48 8b c8 e8 62 75 00 00 48 8b .H.D$XH........H......H...bu..H.
469c0 4c 24 58 85 c0 74 36 48 8b 51 18 48 89 54 24 70 48 85 d2 74 3d 48 8b 59 10 48 8b ca e8 0f 75 00 L$X..t6H.Q.H.T$pH..t=H.Y.H....u.
469e0 00 48 8b cb e8 07 75 00 00 48 8b 4c 24 58 48 89 5c 24 58 e8 d8 74 00 00 48 8b 4c 24 58 48 8b 54 .H....u..H.L$XH.\$X..t..H.L$XH.T
46a00 24 70 48 85 d2 74 0b 4c 8b 45 e8 e8 80 81 fc ff eb 09 48 8b 55 e8 e8 a5 82 fc ff 48 8b 4c 24 70 $pH..t.L.E........H.U......H.L$p
46a20 48 89 44 24 50 e8 76 74 00 00 48 89 7c 24 70 48 39 7c 24 50 0f 84 47 02 00 00 48 8b 4c 24 58 e8 H.D$P.vt..H.|$pH9|$P..G...H.L$X.
46a40 8c 74 00 00 48 8b ce 48 89 7c 24 58 48 8b 74 24 50 48 89 75 e0 e8 76 74 00 00 48 8b 15 47 03 06 .t..H..H.|$XH.t$PH.u..vt..H..G..
46a60 00 48 8b ce e8 e7 8f fc ff 48 89 44 24 50 48 85 c0 0f 84 f4 01 00 00 48 8b 4d 88 48 8b d0 ff 15 .H.......H.D$PH........H.M.H....
46a80 2c 80 00 00 48 89 44 24 58 48 85 c0 0f 84 c3 01 00 00 48 8b 4c 24 50 e8 34 74 00 00 48 8b 4d 18 ,...H.D$XH........H.L$P.4t..H.M.
46aa0 b8 01 00 00 00 89 44 24 48 45 33 c9 89 7c 24 40 48 8d 44 24 58 89 7c 24 38 45 33 c0 48 89 7c 24 ......D$HE3..|$@H.D$X.|$8E3.H.|$
46ac0 30 48 8b d6 48 89 44 24 28 48 8d 45 88 48 89 44 24 20 48 89 7c 24 50 e8 54 6c fc ff 85 c0 0f 88 0H..H.D$(H.E.H.D$.H.|$P.Tl......
46ae0 5b 01 00 00 48 8b 4c 24 58 e8 e2 73 00 00 48 8b 15 b3 02 06 00 48 8b ce 48 89 7c 24 58 e8 4e 8f [...H.L$X..s..H......H..H.|$X.N.
46b00 fc ff 48 89 44 24 58 48 85 c0 0f 84 19 01 00 00 48 8b 4d 88 48 8b d0 ff 15 33 7f 00 00 48 89 44 ..H.D$XH........H.M.H....3...H.D
46b20 24 50 48 85 c0 0f 84 e8 00 00 00 48 8b 4c 24 58 e8 9b 73 00 00 48 8b 44 24 50 48 8b 4d 88 48 89 $PH........H.L$X..s..H.D$PH.M.H.
46b40 45 88 48 89 7c 24 58 e8 84 73 00 00 48 8b 4d 88 45 33 c0 49 8b d6 48 89 7c 24 50 ff 15 0f 7f 00 E.H.|$X..s..H.M.E3.I..H.|$P.....
46b60 00 48 89 44 24 70 48 85 c0 0f 85 51 f6 ff ff bb 0d 03 00 00 41 be 4e 21 00 00 4c 8b ff 4c 8b e7 .H.D$pH....Q........A.N!..L..L..
46b80 e9 23 1b 00 00 bb 10 03 00 00 41 be 8b 21 00 00 4c 8b ff 4c 8b e7 e9 0d 1b 00 00 bb 10 03 00 00 .#........A..!..L..L............
46ba0 41 be 89 21 00 00 4c 8b ff 4c 8b e7 e9 f7 1a 00 00 bb 14 03 00 00 41 be 19 22 00 00 4c 8b ff 4c A..!..L..L............A.."..L..L
46bc0 8b e7 e9 e1 1a 00 00 48 8b 4c 24 68 e8 ff 72 00 00 48 89 7c 24 68 e8 85 6c fc ff 85 c0 75 08 48 .......H.L$h..r..H.|$h..l....u.H
46be0 8b ce e8 39 6d fc ff bb 14 03 00 00 41 be 21 22 00 00 4c 8b ff 4c 8b e7 e9 ab 1a 00 00 bb 14 03 ...9m.......A.!"..L..L..........
46c00 00 00 41 be 11 22 00 00 4c 8b ff 4c 8b e7 e9 95 1a 00 00 bb 18 03 00 00 41 be 76 22 00 00 4c 8b ..A.."..L..L............A.v"..L.
46c20 ff 4c 8b e7 e9 7f 1a 00 00 bb 18 03 00 00 41 be 74 22 00 00 4c 8b ff 4c 8b e7 e9 69 1a 00 00 bb .L............A.t"..L..L...i....
46c40 17 03 00 00 41 be 6a 22 00 00 4c 8b ff 4c 8b e7 e9 53 1a 00 00 bb 17 03 00 00 41 be 67 22 00 00 ....A.j"..L..L...S........A.g"..
46c60 4c 8b ff 4c 8b e7 e9 3d 1a 00 00 bb 17 03 00 00 41 be 65 22 00 00 4c 8b ff 4c 8b e7 e9 27 1a 00 L..L...=........A.e"..L..L...'..
46c80 00 bb 16 03 00 00 41 be 58 22 00 00 4c 8b ff 4c 8b e7 e9 11 1a 00 00 bb 16 03 00 00 41 be 4a 22 ......A.X"..L..L............A.J"
46ca0 00 00 4c 8b ff 4c 8b e7 e9 fb 19 00 00 bb 15 03 00 00 41 be 3e 22 00 00 4c 8b ff 4c 8b e7 e9 e5 ..L..L............A.>"..L..L....
46cc0 19 00 00 bb 15 03 00 00 41 be 30 22 00 00 4c 8b ff 4c 8b e7 e9 cf 19 00 00 7e 0c b9 02 00 00 00 ........A.0"..L..L.......~......
46ce0 e8 7b 6c fc ff eb 0a 48 85 c9 78 05 e8 2f 6c fc ff bb 14 03 00 00 41 be fc 21 00 00 4c 8b ff 4c .{l....H..x../l.......A..!..L..L
46d00 8b e7 e9 a1 19 00 00 bb 14 03 00 00 41 be f1 21 00 00 4c 8b ff 4c 8b e7 e9 8b 19 00 00 bb 14 03 ............A..!..L..L..........
46d20 00 00 41 be f0 21 00 00 4c 8b ff 4c 8b e7 e9 75 19 00 00 bb 14 03 00 00 41 be ee 21 00 00 4c 8b ..A..!..L..L...u........A..!..L.
46d40 ff 4c 8b e7 e9 5f 19 00 00 bb 14 03 00 00 41 be e9 21 00 00 4c 8b ff 4c 8b e7 e9 49 19 00 00 bb .L..._........A..!..L..L...I....
46d60 14 03 00 00 41 be e6 21 00 00 4c 8b ff 4c 8b e7 e9 33 19 00 00 bb 14 03 00 00 41 be e4 21 00 00 ....A..!..L..L...3........A..!..
46d80 4c 8b ff 4c 8b e7 e9 1d 19 00 00 bb 13 03 00 00 41 be d5 21 00 00 4c 8b ff 4c 8b e7 e9 07 19 00 L..L............A..!..L..L......
46da0 00 bb 13 03 00 00 41 be d4 21 00 00 4c 8b ff 4c 8b e7 e9 f1 18 00 00 bb 13 03 00 00 41 be d2 21 ......A..!..L..L............A..!
46dc0 00 00 4c 8b ff 4c 8b e7 e9 db 18 00 00 bb 13 03 00 00 41 be cd 21 00 00 4c 8b ff 4c 8b e7 e9 c5 ..L..L............A..!..L..L....
46de0 18 00 00 bb 13 03 00 00 41 be cb 21 00 00 4c 8b ff 4c 8b e7 e9 af 18 00 00 bb 12 03 00 00 41 be ........A..!..L..L............A.
46e00 be 21 00 00 4c 8b ff 4c 8b e7 e9 99 18 00 00 bb 12 03 00 00 41 be bc 21 00 00 4c 8b ff 4c 8b e7 .!..L..L............A..!..L..L..
46e20 e9 83 18 00 00 bb 11 03 00 00 41 be af 21 00 00 4c 8b ff 4c 8b e7 e9 6d 18 00 00 bb 11 03 00 00 ..........A..!..L..L...m........
46e40 41 be a0 21 00 00 4c 8b ff 4c 8b e7 e9 57 18 00 00 bb 11 03 00 00 41 be 9e 21 00 00 4c 8b ff 4c A..!..L..L...W........A..!..L..L
46e60 8b e7 e9 41 18 00 00 bb 0f 03 00 00 41 be 7e 21 00 00 4c 8b ff 4c 8b e7 e9 2b 18 00 00 bb 0f 03 ...A........A.~!..L..L...+......
46e80 00 00 41 be 7d 21 00 00 4c 8b ff 4c 8b e7 e9 15 18 00 00 bb 0e 03 00 00 41 be 70 21 00 00 4c 8b ..A.}!..L..L............A.p!..L.
46ea0 ff 4c 8b e7 e9 ff 17 00 00 bb 0e 03 00 00 41 be 5e 21 00 00 4c 8b ff 4c 8b e7 e9 e9 17 00 00 bb .L............A.^!..L..L........
46ec0 0e 03 00 00 41 be 5c 21 00 00 4c 8b ff 4c 8b e7 e9 d3 17 00 00 bb 0e 03 00 00 41 be 5a 21 00 00 ....A.\!..L..L............A.Z!..
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55540 72 20 36 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 6d 75 6c 74 69 6e 6f 6d 69 61 r.6:..........>>>.rng.multinomia
55560 6c 28 31 30 30 2c 20 5b 31 2f 37 2e 5d 2a 35 20 2b 20 5b 32 2f 37 2e 5d 29 0a 20 20 20 20 20 20 l(100,.[1/7.]*5.+.[2/7.]).......
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556e0 74 68 65 0a 20 20 20 20 20 20 20 20 66 69 72 73 74 20 68 61 73 20 33 20 6f 75 74 63 6f 6d 65 73 the.........first.has.3.outcomes
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55760 72 61 79 28 5b 5b 30 2c 20 30 2c 20 31 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5b ray([[0,.0,.1],................[
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55c20 0a 20 20 20 20 20 20 20 20 56 61 6c 75 65 45 72 72 6f 72 3a 20 70 76 61 6c 73 20 3c 20 30 2c 20 .........ValueError:.pvals.<.0,.
55c40 70 76 61 6c 73 20 3e 20 31 20 6f 72 20 70 76 61 6c 73 20 63 6f 6e 74 61 69 6e 73 20 4e 61 4e 73 pvals.>.1.or.pvals.contains.NaNs
55c60 0a 20 20 20 20 20 20 20 20 00 00 00 64 6f 75 62 6c 65 00 00 74 6f 6c 00 47 65 6e 65 72 61 74 6f ............double..tol.Generato
55c80 72 2e 67 75 6d 62 65 6c 20 28 6c 69 6e 65 20 32 32 35 39 29 00 00 00 00 63 6f 6c 6c 65 63 74 69 r.gumbel.(line.2259)....collecti
55ca0 6f 6e 73 2e 61 62 63 00 63 6c 69 6e 65 5f 69 6e 5f 74 72 61 63 65 62 61 63 6b 00 00 63 6f 75 6e ons.abc.cline_in_traceback..coun
55cc0 74 00 00 00 63 6f 6c 6f 72 73 00 00 65 70 73 00 3c 73 74 72 69 64 65 64 20 61 6e 64 20 69 6e 64 t...colors..eps.<strided.and.ind
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55d20 70 65 00 00 7a 69 67 00 64 65 66 61 75 6c 74 5f 72 6e 67 20 28 6c 69 6e 65 20 34 36 36 30 29 00 pe..zig.default_rng.(line.4660).
55d40 6c 65 66 74 20 3e 20 6d 6f 64 65 00 00 00 00 00 27 20 6f 62 6a 65 63 74 20 77 68 69 63 68 20 69 left.>.mode.....'.object.which.i
55d60 73 20 6e 6f 74 20 61 20 73 75 62 63 6c 61 73 73 20 6f 66 20 27 53 65 71 75 65 6e 63 65 27 3b 20 s.not.a.subclass.of.'Sequence';.
55d80 60 73 68 75 66 66 6c 65 60 20 69 73 20 6e 6f 74 20 67 75 61 72 61 6e 74 65 65 64 20 74 6f 20 62 `shuffle`.is.not.guaranteed.to.b
55da0 65 68 61 76 65 20 63 6f 72 72 65 63 74 6c 79 2e 20 45 2e 67 2e 2c 20 6e 6f 6e 2d 6e 75 6d 70 79 ehave.correctly..E.g.,.non-numpy
55dc0 20 61 72 72 61 79 2f 74 65 6e 73 6f 72 20 6f 62 6a 65 63 74 73 20 77 69 74 68 20 76 69 65 77 20 .array/tensor.objects.with.view.
55de0 73 65 6d 61 6e 74 69 63 73 20 6d 61 79 20 63 6f 6e 74 61 69 6e 20 64 75 70 6c 69 63 61 74 65 73 semantics.may.contain.duplicates
55e00 20 61 66 74 65 72 20 73 68 75 66 66 6c 69 6e 67 2e 00 00 00 72 69 67 68 74 00 00 00 00 00 00 00 .after.shuffling....right.......
55e20 0a 20 20 20 20 20 20 20 20 63 68 6f 69 63 65 28 61 2c 20 73 69 7a 65 3d 4e 6f 6e 65 2c 20 72 65 .........choice(a,.size=None,.re
55e40 70 6c 61 63 65 3d 54 72 75 65 2c 20 70 3d 4e 6f 6e 65 2c 20 61 78 69 73 3d 30 2c 20 73 68 75 66 place=True,.p=None,.axis=0,.shuf
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55e80 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 66 72 6f 6d 20 61 20 67 69 76 65 6e 20 61 72 72 61 79 0a andom.sample.from.a.given.array.
55ea0 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d .........Parameters.........----
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55ee0 69 6e 74 7d 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 61 6e 20 6e 64 61 72 72 61 79 2c 20 int}.............If.an.ndarray,.
55f00 61 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 69 73 20 67 65 6e 65 72 61 74 65 64 20 66 72 6f a.random.sample.is.generated.fro
55f20 6d 20 69 74 73 20 65 6c 65 6d 65 6e 74 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 61 m.its.elements..............If.a
55f40 6e 20 69 6e 74 2c 20 74 68 65 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 69 73 20 67 65 6e 65 n.int,.the.random.sample.is.gene
55f60 72 61 74 65 64 20 66 72 6f 6d 20 6e 70 2e 61 72 61 6e 67 65 28 61 29 2e 0a 20 20 20 20 20 20 20 rated.from.np.arange(a).........
55f80 20 73 69 7a 65 20 3a 20 7b 69 6e 74 2c 20 74 75 70 6c 65 5b 69 6e 74 5d 7d 2c 20 6f 70 74 69 6f .size.:.{int,.tuple[int]},.optio
55fa0 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 nal.............Output.shape...I
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56000 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 20 66 72 6f 6d *.n.*.k``.samples.are.drawn.from
56020 20 74 68 65 20 31 2d 64 20 60 61 60 2e 20 49 66 20 60 61 60 20 68 61 73 20 6d 6f 72 65 0a 20 20 .the.1-d.`a`..If.`a`.has.more...
56040 20 20 20 20 20 20 20 20 20 20 74 68 61 6e 20 6f 6e 65 20 64 69 6d 65 6e 73 69 6f 6e 2c 20 74 68 ..........than.one.dimension,.th
56060 65 20 60 73 69 7a 65 60 20 73 68 61 70 65 20 77 69 6c 6c 20 62 65 20 69 6e 73 65 72 74 65 64 20 e.`size`.shape.will.be.inserted.
56080 69 6e 74 6f 20 74 68 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 61 78 69 73 60 20 64 69 6d 65 into.the.............`axis`.dime
560a0 6e 73 69 6f 6e 2c 20 73 6f 20 74 68 65 20 6f 75 74 70 75 74 20 60 60 6e 64 69 6d 60 60 20 77 69 nsion,.so.the.output.``ndim``.wi
560c0 6c 6c 20 62 65 20 60 60 61 2e 6e 64 69 6d 20 2d 20 31 20 2b 0a 20 20 20 20 20 20 20 20 20 20 20 ll.be.``a.ndim.-.1.+............
560e0 20 6c 65 6e 28 73 69 7a 65 29 60 60 2e 20 44 65 66 61 75 6c 74 20 69 73 20 4e 6f 6e 65 2c 20 69 .len(size)``..Default.is.None,.i
56100 6e 20 77 68 69 63 68 20 63 61 73 65 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 0a 20 n.which.case.a.single.value.is..
56120 20 20 20 20 20 20 20 20 20 20 20 72 65 74 75 72 6e 65 64 2e 0a 20 20 20 20 20 20 20 20 72 65 70 ...........returned..........rep
56140 6c 61 63 65 20 3a 20 62 6f 6f 6c 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 lace.:.bool,.optional...........
56160 20 20 57 68 65 74 68 65 72 20 74 68 65 20 73 61 6d 70 6c 65 20 69 73 20 77 69 74 68 20 6f 72 20 ..Whether.the.sample.is.with.or.
56180 77 69 74 68 6f 75 74 20 72 65 70 6c 61 63 65 6d 65 6e 74 2e 20 44 65 66 61 75 6c 74 20 69 73 20 without.replacement..Default.is.
561a0 54 72 75 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 6d 65 61 6e 69 6e 67 20 74 68 61 74 20 61 True,.............meaning.that.a
561c0 20 76 61 6c 75 65 20 6f 66 20 60 60 61 60 60 20 63 61 6e 20 62 65 20 73 65 6c 65 63 74 65 64 20 .value.of.``a``.can.be.selected.
561e0 6d 75 6c 74 69 70 6c 65 20 74 69 6d 65 73 2e 0a 20 20 20 20 20 20 20 20 70 20 3a 20 31 2d 44 20 multiple.times..........p.:.1-D.
56200 61 72 72 61 79 5f 6c 69 6b 65 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 array_like,.optional............
56220 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 69 65 73 20 61 73 73 6f 63 69 61 74 65 64 20 77 69 .The.probabilities.associated.wi
56240 74 68 20 65 61 63 68 20 65 6e 74 72 79 20 69 6e 20 61 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 th.each.entry.in.a..............
56260 49 66 20 6e 6f 74 20 67 69 76 65 6e 2c 20 74 68 65 20 73 61 6d 70 6c 65 20 61 73 73 75 6d 65 73 If.not.given,.the.sample.assumes
56280 20 61 20 75 6e 69 66 6f 72 6d 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 6f 76 65 72 20 61 6c 6c .a.uniform.distribution.over.all
562a0 0a 20 20 20 20 20 20 20 20 20 20 20 20 65 6e 74 72 69 65 73 20 69 6e 20 60 60 61 60 60 2e 0a 20 .............entries.in.``a``...
562c0 20 20 20 20 20 20 20 61 78 69 73 20 3a 20 69 6e 74 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 .......axis.:.int,.optional.....
562e0 20 20 20 20 20 20 20 20 54 68 65 20 61 78 69 73 20 61 6c 6f 6e 67 20 77 68 69 63 68 20 74 68 65 ........The.axis.along.which.the
56300 20 73 65 6c 65 63 74 69 6f 6e 20 69 73 20 70 65 72 66 6f 72 6d 65 64 2e 20 54 68 65 20 64 65 66 .selection.is.performed..The.def
56320 61 75 6c 74 2c 20 30 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 73 65 6c 65 63 74 73 20 62 79 20 ault,.0,.............selects.by.
56340 72 6f 77 2e 0a 20 20 20 20 20 20 20 20 73 68 75 66 66 6c 65 20 3a 20 62 6f 6f 6c 2c 20 6f 70 74 row..........shuffle.:.bool,.opt
56360 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 57 68 65 74 68 65 72 20 74 68 65 20 73 61 ional.............Whether.the.sa
56380 6d 70 6c 65 20 69 73 20 73 68 75 66 66 6c 65 64 20 77 68 65 6e 20 73 61 6d 70 6c 69 6e 67 20 77 mple.is.shuffled.when.sampling.w
563a0 69 74 68 6f 75 74 20 72 65 70 6c 61 63 65 6d 65 6e 74 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 ithout.replacement..............
563c0 44 65 66 61 75 6c 74 20 69 73 20 54 72 75 65 2c 20 46 61 6c 73 65 20 70 72 6f 76 69 64 65 73 20 Default.is.True,.False.provides.
563e0 61 20 73 70 65 65 64 75 70 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 a.speedup...........Returns.....
56400 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 61 6d 70 6c 65 73 20 3a 20 73 69 ....-------.........samples.:.si
56420 6e 67 6c 65 20 69 74 65 6d 20 6f 72 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 20 20 20 ngle.item.or.ndarray............
56440 20 54 68 65 20 67 65 6e 65 72 61 74 65 64 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 73 0a 0a 20 .The.generated.random.samples...
56460 20 20 20 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 .......Raises.........------....
56480 20 20 20 20 20 56 61 6c 75 65 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 61 .....ValueError.............If.a
564a0 20 69 73 20 61 6e 20 69 6e 74 20 61 6e 64 20 6c 65 73 73 20 74 68 61 6e 20 7a 65 72 6f 2c 20 69 .is.an.int.and.less.than.zero,.i
564c0 66 20 70 20 69 73 20 6e 6f 74 20 31 2d 64 69 6d 65 6e 73 69 6f 6e 61 6c 2c 20 69 66 0a 20 20 20 f.p.is.not.1-dimensional,.if....
564e0 20 20 20 20 20 20 20 20 20 61 20 69 73 20 61 72 72 61 79 2d 6c 69 6b 65 20 77 69 74 68 20 61 20 .........a.is.array-like.with.a.
56500 73 69 7a 65 20 30 2c 20 69 66 20 70 20 69 73 20 6e 6f 74 20 61 20 76 65 63 74 6f 72 20 6f 66 0a size.0,.if.p.is.not.a.vector.of.
56520 20 20 20 20 20 20 20 20 20 20 20 20 70 72 6f 62 61 62 69 6c 69 74 69 65 73 2c 20 69 66 20 61 20 ............probabilities,.if.a.
56540 61 6e 64 20 70 20 68 61 76 65 20 64 69 66 66 65 72 65 6e 74 20 6c 65 6e 67 74 68 73 2c 20 6f 72 and.p.have.different.lengths,.or
56560 20 69 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 72 65 70 6c 61 63 65 3d 46 61 6c 73 65 20 61 6e .if.............replace=False.an
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565a0 6e 20 74 68 65 20 70 6f 70 75 6c 61 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 73 69 7a n.the.population.............siz
565c0 65 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d e...........See.Also.........---
565e0 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 69 6e 74 65 67 65 72 73 2c 20 73 68 75 66 66 6c 65 2c -----.........integers,.shuffle,
56600 20 70 65 72 6d 75 74 61 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 .permutation..........Notes.....
56620 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 53 65 74 74 69 6e 67 20 75 73 65 72 2d 73 ....-----.........Setting.user-s
56640 70 65 63 69 66 69 65 64 20 70 72 6f 62 61 62 69 6c 69 74 69 65 73 20 74 68 72 6f 75 67 68 20 60 pecified.probabilities.through.`
56660 60 70 60 60 20 75 73 65 73 20 61 20 6d 6f 72 65 20 67 65 6e 65 72 61 6c 20 62 75 74 20 6c 65 73 `p``.uses.a.more.general.but.les
56680 73 0a 20 20 20 20 20 20 20 20 65 66 66 69 63 69 65 6e 74 20 73 61 6d 70 6c 65 72 20 74 68 61 6e s.........efficient.sampler.than
566a0 20 74 68 65 20 64 65 66 61 75 6c 74 2e 20 54 68 65 20 67 65 6e 65 72 61 6c 20 73 61 6d 70 6c 65 .the.default..The.general.sample
566c0 72 20 70 72 6f 64 75 63 65 73 20 61 20 64 69 66 66 65 72 65 6e 74 20 73 61 6d 70 6c 65 0a 20 20 r.produces.a.different.sample...
566e0 20 20 20 20 20 20 74 68 61 6e 20 74 68 65 20 6f 70 74 69 6d 69 7a 65 64 20 73 61 6d 70 6c 65 72 ......than.the.optimized.sampler
56700 20 65 76 65 6e 20 69 66 20 65 61 63 68 20 65 6c 65 6d 65 6e 74 20 6f 66 20 60 60 70 60 60 20 69 .even.if.each.element.of.``p``.i
56720 73 20 31 20 2f 20 6c 65 6e 28 61 29 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a s.1./.len(a)...........Examples.
56740 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 74 ........--------.........Generat
56760 65 20 61 20 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 66 72 6f 6d 20 6e e.a.uniform.random.sample.from.n
56780 70 2e 61 72 61 6e 67 65 28 35 29 20 6f 66 20 73 69 7a 65 20 33 3a 0a 0a 20 20 20 20 20 20 20 20 p.arange(5).of.size.3:..........
567a0 3e 3e 3e 20 72 6e 67 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 >>>.rng.=.np.random.default_rng(
567c0 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 35 2c 20 33 29 0a 20 ).........>>>.rng.choice(5,.3)..
567e0 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 30 2c 20 33 2c 20 34 5d 29 20 23 20 72 61 6e 64 6f 6d .......array([0,.3,.4]).#.random
56800 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 23 54 68 69 73 20 69 73 20 65 71 75 69 76 61 6c 65 6e 74 .........>>>.#This.is.equivalent
56820 20 74 6f 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 30 2c 35 2c 33 29 0a 0a 20 20 20 20 20 20 20 .to.rng.integers(0,5,3).........
56840 20 47 65 6e 65 72 61 74 65 20 61 20 6e 6f 6e 2d 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 .Generate.a.non-uniform.random.s
56860 61 6d 70 6c 65 20 66 72 6f 6d 20 6e 70 2e 61 72 61 6e 67 65 28 35 29 20 6f 66 20 73 69 7a 65 20 ample.from.np.arange(5).of.size.
56880 33 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 35 2c 20 33 2c 3:..........>>>.rng.choice(5,.3,
568a0 20 70 3d 5b 30 2e 31 2c 20 30 2c 20 30 2e 33 2c 20 30 2e 36 2c 20 30 5d 29 0a 20 20 20 20 20 20 .p=[0.1,.0,.0.3,.0.6,.0]).......
568c0 20 20 61 72 72 61 79 28 5b 33 2c 20 33 2c 20 30 5d 29 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 ..array([3,.3,.0]).#.random.....
568e0 20 20 20 20 20 47 65 6e 65 72 61 74 65 20 61 20 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 .....Generate.a.uniform.random.s
56900 61 6d 70 6c 65 20 66 72 6f 6d 20 6e 70 2e 61 72 61 6e 67 65 28 35 29 20 6f 66 20 73 69 7a 65 20 ample.from.np.arange(5).of.size.
56920 33 20 77 69 74 68 6f 75 74 0a 20 20 20 20 20 20 20 20 72 65 70 6c 61 63 65 6d 65 6e 74 3a 0a 0a 3.without.........replacement:..
56940 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 35 2c 20 33 2c 20 72 65 70 ........>>>.rng.choice(5,.3,.rep
56960 6c 61 63 65 3d 46 61 6c 73 65 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 33 2c 31 2c 30 lace=False).........array([3,1,0
56980 5d 29 20 23 20 72 61 6e 64 6f 6d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 23 54 68 69 73 20 69 73 ]).#.random.........>>>.#This.is
569a0 20 65 71 75 69 76 61 6c 65 6e 74 20 74 6f 20 72 6e 67 2e 70 65 72 6d 75 74 61 74 69 6f 6e 28 6e .equivalent.to.rng.permutation(n
569c0 70 2e 61 72 61 6e 67 65 28 35 29 29 5b 3a 33 5d 0a 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 p.arange(5))[:3]..........Genera
569e0 74 65 20 61 20 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 66 72 6f 6d 20 te.a.uniform.random.sample.from.
56a00 61 20 32 2d 44 20 61 72 72 61 79 20 61 6c 6f 6e 67 20 74 68 65 20 66 69 72 73 74 0a 20 20 20 20 a.2-D.array.along.the.first.....
56a20 20 20 20 20 61 78 69 73 20 28 74 68 65 20 64 65 66 61 75 6c 74 29 2c 20 77 69 74 68 6f 75 74 20 ....axis.(the.default),.without.
56a40 72 65 70 6c 61 63 65 6d 65 6e 74 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 replacement:..........>>>.rng.ch
56a60 6f 69 63 65 28 5b 5b 30 2c 20 31 2c 20 32 5d 2c 20 5b 33 2c 20 34 2c 20 35 5d 2c 20 5b 36 2c 20 oice([[0,.1,.2],.[3,.4,.5],.[6,.
56a80 37 2c 20 38 5d 5d 2c 20 32 2c 20 72 65 70 6c 61 63 65 3d 46 61 6c 73 65 29 0a 20 20 20 20 20 20 7,.8]],.2,.replace=False).......
56aa0 20 20 61 72 72 61 79 28 5b 5b 33 2c 20 34 2c 20 35 5d 2c 20 23 20 72 61 6e 64 6f 6d 0a 20 20 20 ..array([[3,.4,.5],.#.random....
56ac0 20 20 20 20 20 20 20 20 20 20 20 20 5b 30 2c 20 31 2c 20 32 5d 5d 29 0a 0a 20 20 20 20 20 20 20 ............[0,.1,.2]]).........
56ae0 20 47 65 6e 65 72 61 74 65 20 61 20 6e 6f 6e 2d 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 .Generate.a.non-uniform.random.s
56b00 61 6d 70 6c 65 20 66 72 6f 6d 20 6e 70 2e 61 72 61 6e 67 65 28 35 29 20 6f 66 20 73 69 7a 65 0a ample.from.np.arange(5).of.size.
56b20 20 20 20 20 20 20 20 20 33 20 77 69 74 68 6f 75 74 20 72 65 70 6c 61 63 65 6d 65 6e 74 3a 0a 0a ........3.without.replacement:..
56b40 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 35 2c 20 33 2c 20 72 65 70 ........>>>.rng.choice(5,.3,.rep
56b60 6c 61 63 65 3d 46 61 6c 73 65 2c 20 70 3d 5b 30 2e 31 2c 20 30 2c 20 30 2e 33 2c 20 30 2e 36 2c lace=False,.p=[0.1,.0,.0.3,.0.6,
56b80 20 30 5d 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 32 2c 20 33 2c 20 30 5d 29 20 23 20 .0]).........array([2,.3,.0]).#.
56ba0 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 41 6e 79 20 6f 66 20 74 68 65 20 61 62 6f 76 65 random..........Any.of.the.above
56bc0 20 63 61 6e 20 62 65 20 72 65 70 65 61 74 65 64 20 77 69 74 68 20 61 6e 20 61 72 62 69 74 72 61 .can.be.repeated.with.an.arbitra
56be0 72 79 20 61 72 72 61 79 2d 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 69 6e 73 74 65 61 64 20 6f 66 ry.array-like.........instead.of
56c00 20 6a 75 73 74 20 69 6e 74 65 67 65 72 73 2e 20 46 6f 72 20 69 6e 73 74 61 6e 63 65 3a 0a 0a 20 .just.integers..For.instance:...
56c20 20 20 20 20 20 20 20 3e 3e 3e 20 61 61 5f 6d 69 6c 6e 65 5f 61 72 72 20 3d 20 5b 27 70 6f 6f 68 .......>>>.aa_milne_arr.=.['pooh
56c40 27 2c 20 27 72 61 62 62 69 74 27 2c 20 27 70 69 67 6c 65 74 27 2c 20 27 43 68 72 69 73 74 6f 70 ',.'rabbit',.'piglet',.'Christop
56c60 68 65 72 27 5d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 61 61 5f her'].........>>>.rng.choice(aa_
56c80 6d 69 6c 6e 65 5f 61 72 72 2c 20 35 2c 20 70 3d 5b 30 2e 35 2c 20 30 2e 31 2c 20 30 2e 31 2c 20 milne_arr,.5,.p=[0.5,.0.1,.0.1,.
56ca0 30 2e 33 5d 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 27 70 6f 6f 68 27 2c 20 27 70 6f 0.3]).........array(['pooh',.'po
56cc0 6f 68 27 2c 20 27 70 6f 6f 68 27 2c 20 27 43 68 72 69 73 74 6f 70 68 65 72 27 2c 20 27 70 69 67 oh',.'pooh',.'Christopher',.'pig
56ce0 6c 65 74 27 5d 2c 20 23 20 72 61 6e 64 6f 6d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 64 74 let'],.#.random...............dt
56d00 79 70 65 3d 27 3c 55 31 31 27 29 0a 0a 20 20 20 20 20 20 20 20 00 00 00 72 61 76 65 6c 00 00 00 ype='<U11').............ravel...
56d20 47 65 6e 65 72 61 74 6f 72 2e 69 6e 74 65 67 65 72 73 20 28 6c 69 6e 65 20 34 34 32 29 00 00 00 Generator.integers.(line.442)...
56d40 6d 61 72 67 69 6e 61 6c 73 00 00 00 69 67 6e 6f 72 65 00 00 63 00 00 00 b0 c0 07 80 01 00 00 00 marginals...ignore..c...........
56d60 c0 c0 07 80 01 00 00 00 d0 c0 07 80 01 00 00 00 e0 c0 07 80 01 00 00 00 f8 c0 07 80 01 00 00 00 ................................
56d80 18 c1 07 80 01 00 00 00 28 c1 07 80 01 00 00 00 68 69 67 68 20 2d 20 6c 6f 77 20 72 61 6e 67 65 ........(.......high.-.low.range
56da0 20 65 78 63 65 65 64 73 20 76 61 6c 69 64 20 62 6f 75 6e 64 73 00 00 00 72 61 69 73 65 00 00 00 .exceeds.valid.bounds...raise...
56dc0 70 76 61 6c 73 20 6d 75 73 74 20 68 61 76 65 20 61 74 20 6c 65 61 73 74 20 31 20 64 69 6d 65 6e pvals.must.have.at.least.1.dimen
56de0 73 69 6f 6e 20 61 6e 64 20 74 68 65 20 6c 61 73 74 20 64 69 6d 65 6e 73 69 6f 6e 20 6f 66 20 70 sion.and.the.last.dimension.of.p
56e00 76 61 6c 73 20 6d 75 73 74 20 62 65 20 67 72 65 61 74 65 72 20 74 68 61 6e 20 30 2e 00 00 00 00 vals.must.be.greater.than.0.....
56e20 47 65 6e 65 72 61 74 6f 72 2e 6c 6f 67 73 65 72 69 65 73 20 28 6c 69 6e 65 20 33 33 38 32 29 00 Generator.logseries.(line.3382).
56e40 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 72 64 5f 6e 6f 72 6d 61 6c 20 28 6c 69 6e 65 20 Generator.standard_normal.(line.
56e60 39 36 37 29 00 00 00 00 6e 73 61 6d 70 6c 65 00 49 6e 64 69 72 65 63 74 20 64 69 6d 65 6e 73 69 967)....nsample.Indirect.dimensi
56e80 6f 6e 73 20 6e 6f 74 20 73 75 70 70 6f 72 74 65 64 00 00 00 4f 00 00 00 47 65 6e 65 72 61 74 6f ons.not.supported...O...Generato
56ea0 72 2e 6e 6f 72 6d 61 6c 20 28 6c 69 6e 65 20 31 30 33 37 29 00 00 00 00 3c 63 6f 6e 74 69 67 75 r.normal.(line.1037)....<contigu
56ec0 6f 75 73 20 61 6e 64 20 69 6e 64 69 72 65 63 74 3e 00 00 00 63 6f 76 00 6c 6f 67 69 63 61 6c 5f ous.and.indirect>...cov.logical_
56ee0 6f 72 00 00 6c 6f 63 00 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 76 61 72 69 61 74 65 5f 6e or..loc.Generator.multivariate_n
56f00 6f 72 6d 61 6c 20 28 6c 69 6e 65 20 33 34 36 33 29 00 00 00 72 61 6e 64 6f 6d 00 00 41 00 00 00 ormal.(line.3463)...random..A...
56f20 5f 5f 73 65 74 73 74 61 74 65 5f 63 79 74 68 6f 6e 5f 5f 00 61 6c 6c 00 46 65 77 65 72 20 6e 6f __setstate_cython__.all.Fewer.no
56f40 6e 2d 7a 65 72 6f 20 65 6e 74 72 69 65 73 20 69 6e 20 70 20 74 68 61 6e 20 73 69 7a 65 00 00 00 n-zero.entries.in.p.than.size...
56f60 6e 75 6d 70 79 00 00 00 43 61 6e 6e 6f 74 20 61 73 73 69 67 6e 20 74 6f 20 72 65 61 64 2d 6f 6e numpy...Cannot.assign.to.read-on
56f80 6c 79 20 6d 65 6d 6f 72 79 76 69 65 77 00 00 00 0a 20 20 20 20 20 20 20 20 6e 6f 72 6d 61 6c 28 ly.memoryview............normal(
56fa0 6c 6f 63 3d 30 2e 30 2c 20 73 63 61 6c 65 3d 31 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a loc=0.0,.scale=1.0,.size=None)..
56fc0 20 20 20 20 20 20 20 20 44 72 61 77 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d ........Draw.random.samples.from
56fe0 20 61 20 6e 6f 72 6d 61 6c 20 28 47 61 75 73 73 69 61 6e 29 20 64 69 73 74 72 69 62 75 74 69 6f .a.normal.(Gaussian).distributio
57000 6e 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 n...........The.probability.dens
57020 69 74 79 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 74 68 65 20 6e 6f 72 6d 61 6c 20 64 69 73 74 72 ity.function.of.the.normal.distr
57040 69 62 75 74 69 6f 6e 2c 20 66 69 72 73 74 0a 20 20 20 20 20 20 20 20 64 65 72 69 76 65 64 20 62 ibution,.first.........derived.b
57060 79 20 44 65 20 4d 6f 69 76 72 65 20 61 6e 64 20 32 30 30 20 79 65 61 72 73 20 6c 61 74 65 72 20 y.De.Moivre.and.200.years.later.
57080 62 79 20 62 6f 74 68 20 47 61 75 73 73 20 61 6e 64 20 4c 61 70 6c 61 63 65 0a 20 20 20 20 20 20 by.both.Gauss.and.Laplace.......
570a0 20 20 69 6e 64 65 70 65 6e 64 65 6e 74 6c 79 20 5b 32 5d 5f 2c 20 69 73 20 6f 66 74 65 6e 20 63 ..independently.[2]_,.is.often.c
570c0 61 6c 6c 65 64 20 74 68 65 20 62 65 6c 6c 20 63 75 72 76 65 20 62 65 63 61 75 73 65 20 6f 66 0a alled.the.bell.curve.because.of.
570e0 20 20 20 20 20 20 20 20 69 74 73 20 63 68 61 72 61 63 74 65 72 69 73 74 69 63 20 73 68 61 70 65 ........its.characteristic.shape
57100 20 28 73 65 65 20 74 68 65 20 65 78 61 6d 70 6c 65 20 62 65 6c 6f 77 29 2e 0a 0a 20 20 20 20 20 .(see.the.example.below)........
57120 20 20 20 54 68 65 20 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 73 20 6f 63 63 75 ...The.normal.distributions.occu
57140 72 73 20 6f 66 74 65 6e 20 69 6e 20 6e 61 74 75 72 65 2e 20 20 46 6f 72 20 65 78 61 6d 70 6c 65 rs.often.in.nature...For.example
57160 2c 20 69 74 0a 20 20 20 20 20 20 20 20 64 65 73 63 72 69 62 65 73 20 74 68 65 20 63 6f 6d 6d 6f ,.it.........describes.the.commo
57180 6e 6c 79 20 6f 63 63 75 72 72 69 6e 67 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 6f 66 20 73 61 nly.occurring.distribution.of.sa
571a0 6d 70 6c 65 73 20 69 6e 66 6c 75 65 6e 63 65 64 0a 20 20 20 20 20 20 20 20 62 79 20 61 20 6c 61 mples.influenced.........by.a.la
571c0 72 67 65 20 6e 75 6d 62 65 72 20 6f 66 20 74 69 6e 79 2c 20 72 61 6e 64 6f 6d 20 64 69 73 74 75 rge.number.of.tiny,.random.distu
571e0 72 62 61 6e 63 65 73 2c 20 65 61 63 68 20 77 69 74 68 20 69 74 73 20 6f 77 6e 0a 20 20 20 20 20 rbances,.each.with.its.own......
57200 20 20 20 75 6e 69 71 75 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 5b 32 5d 5f 2e 0a 0a 20 20 ...unique.distribution.[2]_.....
57220 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d ......Parameters.........-------
57240 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6c 6f 63 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 ---.........loc.:.float.or.array
57260 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 4d 65 61 6e _like.of.floats.............Mean
57280 20 28 22 63 65 6e 74 72 65 22 29 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e .("centre").of.the.distribution.
572a0 0a 20 20 20 20 20 20 20 20 73 63 61 6c 65 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f .........scale.:.float.or.array_
572c0 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 53 74 61 6e 64 like.of.floats.............Stand
572e0 61 72 64 20 64 65 76 69 61 74 69 6f 6e 20 28 73 70 72 65 61 64 20 6f 72 20 22 77 69 64 74 68 22 ard.deviation.(spread.or."width"
57300 29 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 4d 75 73 74 20 62 65 0a 20 ).of.the.distribution..Must.be..
57320 20 20 20 20 20 20 20 20 20 20 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 2e 0a 20 20 20 20 20 20 20 ...........non-negative.........
57340 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 .size.:.int.or.tuple.of.ints,.op
57360 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e tional.............Output.shape.
57380 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 ..If.the.given.shape.is,.e.g.,.`
573a0 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 `(m,.n,.k)``,.then.............`
573c0 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 `m.*.n.*.k``.samples.are.drawn..
573e0 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a .If.size.is.``None``.(default),.
57400 20 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 ............a.single.value.is.re
57420 74 75 72 6e 65 64 20 69 66 20 60 60 6c 6f 63 60 60 20 61 6e 64 20 60 60 73 63 61 6c 65 60 60 20 turned.if.``loc``.and.``scale``.
57440 61 72 65 20 62 6f 74 68 20 73 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 are.both.scalars..............Ot
57460 68 65 72 77 69 73 65 2c 20 60 60 6e 70 2e 62 72 6f 61 64 63 61 73 74 28 6c 6f 63 2c 20 73 63 61 herwise,.``np.broadcast(loc,.sca
57480 6c 65 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 le).size``.samples.are.drawn....
574a0 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 .......Returns.........-------..
574c0 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 .......out.:.ndarray.or.scalar..
574e0 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 ...........Drawn.samples.from.th
57500 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 e.parameterized.normal.distribut
57520 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d ion...........See.Also.........-
57540 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 6e 6f 72 6d -------.........scipy.stats.norm
57560 20 3a 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c .:.probability.density.function,
57580 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 6f 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 63 75 6d .distribution.or.............cum
575a0 75 6c 61 74 69 76 65 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 65 74 63 2e 0a 0a ulative.density.function,.etc...
575c0 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 ........Notes.........-----.....
575e0 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 6f 72 20 ....The.probability.density.for.
57600 74 68 65 20 47 61 75 73 73 69 61 6e 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 0a 0a 20 20 the.Gaussian.distribution.is....
57620 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 5c 66 72 61 63 7b 31 7d 7b .........math::.p(x).=.\frac{1}{
57640 5c 73 71 72 74 7b 20 32 20 5c 70 69 20 5c 73 69 67 6d 61 5e 32 20 7d 7d 0a 20 20 20 20 20 20 20 \sqrt{.2.\pi.\sigma^2.}}........
57660 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 65 5e 7b 20 2d 20 5c 66 72 61 63 7b 20 28 ..................e^{.-.\frac{.(
57680 78 20 2d 20 5c 6d 75 29 5e 32 20 7d 20 7b 32 20 5c 73 69 67 6d 61 5e 32 7d 20 7d 2c 0a 0a 20 20 x.-.\mu)^2.}.{2.\sigma^2}.},....
576a0 20 20 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 5c 6d 75 60 20 69 73 20 74 68 65 20 6d ......where.:math:`\mu`.is.the.m
576c0 65 61 6e 20 61 6e 64 20 3a 6d 61 74 68 3a 60 5c 73 69 67 6d 61 60 20 74 68 65 20 73 74 61 6e 64 ean.and.:math:`\sigma`.the.stand
576e0 61 72 64 0a 20 20 20 20 20 20 20 20 64 65 76 69 61 74 69 6f 6e 2e 20 54 68 65 20 73 71 75 61 72 ard.........deviation..The.squar
57700 65 20 6f 66 20 74 68 65 20 73 74 61 6e 64 61 72 64 20 64 65 76 69 61 74 69 6f 6e 2c 20 3a 6d 61 e.of.the.standard.deviation,.:ma
57720 74 68 3a 60 5c 73 69 67 6d 61 5e 32 60 2c 0a 20 20 20 20 20 20 20 20 69 73 20 63 61 6c 6c 65 64 th:`\sigma^2`,.........is.called
57740 20 74 68 65 20 76 61 72 69 61 6e 63 65 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 66 75 6e 63 .the.variance...........The.func
57760 74 69 6f 6e 20 68 61 73 20 69 74 73 20 70 65 61 6b 20 61 74 20 74 68 65 20 6d 65 61 6e 2c 20 61 tion.has.its.peak.at.the.mean,.a
57780 6e 64 20 69 74 73 20 22 73 70 72 65 61 64 22 20 69 6e 63 72 65 61 73 65 73 20 77 69 74 68 0a 20 nd.its."spread".increases.with..
577a0 20 20 20 20 20 20 20 74 68 65 20 73 74 61 6e 64 61 72 64 20 64 65 76 69 61 74 69 6f 6e 20 28 74 .......the.standard.deviation.(t
577c0 68 65 20 66 75 6e 63 74 69 6f 6e 20 72 65 61 63 68 65 73 20 30 2e 36 30 37 20 74 69 6d 65 73 20 he.function.reaches.0.607.times.
577e0 69 74 73 20 6d 61 78 69 6d 75 6d 20 61 74 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 78 20 its.maximum.at.........:math:`x.
57800 2b 20 5c 73 69 67 6d 61 60 20 61 6e 64 20 3a 6d 61 74 68 3a 60 78 20 2d 20 5c 73 69 67 6d 61 60 +.\sigma`.and.:math:`x.-.\sigma`
57820 20 5b 32 5d 5f 29 2e 20 20 54 68 69 73 20 69 6d 70 6c 69 65 73 20 74 68 61 74 0a 20 20 20 20 20 .[2]_)...This.implies.that......
57840 20 20 20 3a 6d 65 74 68 3a 60 6e 6f 72 6d 61 6c 60 20 69 73 20 6d 6f 72 65 20 6c 69 6b 65 6c 79 ...:meth:`normal`.is.more.likely
57860 20 74 6f 20 72 65 74 75 72 6e 20 73 61 6d 70 6c 65 73 20 6c 79 69 6e 67 20 63 6c 6f 73 65 20 74 .to.return.samples.lying.close.t
57880 6f 20 74 68 65 0a 20 20 20 20 20 20 20 20 6d 65 61 6e 2c 20 72 61 74 68 65 72 20 74 68 61 6e 20 o.the.........mean,.rather.than.
578a0 74 68 6f 73 65 20 66 61 72 20 61 77 61 79 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e those.far.away...........Referen
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58ac0 64 72 69 6c 6c 73 20 39 20 77 69 6c 64 2d 63 61 74 20 6f 69 6c 20 65 78 70 6c 6f 72 61 74 69 6f drills.9.wild-cat.oil.exploratio
58ae0 6e 0a 20 20 20 20 20 20 20 20 77 65 6c 6c 73 2c 20 65 61 63 68 20 77 69 74 68 20 61 6e 20 65 73 n.........wells,.each.with.an.es
58b00 74 69 6d 61 74 65 64 20 70 72 6f 62 61 62 69 6c 69 74 79 20 6f 66 20 73 75 63 63 65 73 73 20 6f timated.probability.of.success.o
58b20 66 20 30 2e 31 2e 20 41 6c 6c 20 6e 69 6e 65 0a 20 20 20 20 20 20 20 20 77 65 6c 6c 73 20 66 61 f.0.1..All.nine.........wells.fa
58b40 69 6c 2e 20 57 68 61 74 20 69 73 20 74 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 6f 66 20 74 il..What.is.the.probability.of.t
58b60 68 61 74 20 68 61 70 70 65 6e 69 6e 67 3f 0a 0a 20 20 20 20 20 20 20 20 4c 65 74 27 73 20 64 6f hat.happening?..........Let's.do
58b80 20 32 30 2c 30 30 30 20 74 72 69 61 6c 73 20 6f 66 20 74 68 65 20 6d 6f 64 65 6c 2c 20 61 6e 64 .20,000.trials.of.the.model,.and
58ba0 20 63 6f 75 6e 74 20 74 68 65 20 6e 75 6d 62 65 72 20 74 68 61 74 0a 20 20 20 20 20 20 20 20 67 .count.the.number.that.........g
58bc0 65 6e 65 72 61 74 65 20 7a 65 72 6f 20 70 6f 73 69 74 69 76 65 20 72 65 73 75 6c 74 73 2e 0a 0a enerate.zero.positive.results...
58be0 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 75 6d 28 72 6e 67 2e 62 69 6e 6f 6d 69 61 6c 28 39 2c 20 ........>>>.sum(rng.binomial(9,.
58c00 30 2e 31 2c 20 32 30 30 30 30 29 20 3d 3d 20 30 29 2f 32 30 30 30 30 2e 0a 20 20 20 20 20 20 20 0.1,.20000).==.0)/20000.........
58c20 20 23 20 61 6e 73 77 65 72 20 3d 20 30 2e 33 38 38 38 35 2c 20 6f 72 20 33 39 25 2e 0a 0a 20 20 .#.answer.=.0.38885,.or.39%.....
58c40 20 20 20 20 20 20 00 00 6c 65 73 73 00 00 00 00 0a 20 20 20 20 20 20 20 20 77 65 69 62 75 6c 6c ........less.............weibull
58c60 28 61 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d (a,.size=None)..........Draw.sam
58c80 70 6c 65 73 20 66 72 6f 6d 20 61 20 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e ples.from.a.Weibull.distribution
58ca0 2e 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 31 ...........Draw.samples.from.a.1
58cc0 2d 70 61 72 61 6d 65 74 65 72 20 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 -parameter.Weibull.distribution.
58ce0 77 69 74 68 20 74 68 65 20 67 69 76 65 6e 0a 20 20 20 20 20 20 20 20 73 68 61 70 65 20 70 61 72 with.the.given.........shape.par
58d00 61 6d 65 74 65 72 20 60 61 60 2e 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 58 ameter.`a`..............math::.X
58d20 20 3d 20 28 2d 6c 6e 28 55 29 29 5e 7b 31 2f 61 7d 0a 0a 20 20 20 20 20 20 20 20 48 65 72 65 2c .=.(-ln(U))^{1/a}..........Here,
58d40 20 55 20 69 73 20 64 72 61 77 6e 20 66 72 6f 6d 20 74 68 65 20 75 6e 69 66 6f 72 6d 20 64 69 73 .U.is.drawn.from.the.uniform.dis
58d60 74 72 69 62 75 74 69 6f 6e 20 6f 76 65 72 20 28 30 2c 31 5d 2e 0a 0a 20 20 20 20 20 20 20 20 54 tribution.over.(0,1]...........T
58d80 68 65 20 6d 6f 72 65 20 63 6f 6d 6d 6f 6e 20 32 2d 70 61 72 61 6d 65 74 65 72 20 57 65 69 62 75 he.more.common.2-parameter.Weibu
58da0 6c 6c 2c 20 69 6e 63 6c 75 64 69 6e 67 20 61 20 73 63 61 6c 65 20 70 61 72 61 6d 65 74 65 72 0a ll,.including.a.scale.parameter.
58dc0 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 5c 6c 61 6d 62 64 61 60 20 69 73 20 6a 75 73 74 20 ........:math:`\lambda`.is.just.
58de0 3a 6d 61 74 68 3a 60 58 20 3d 20 5c 6c 61 6d 62 64 61 28 2d 6c 6e 28 55 29 29 5e 7b 31 2f 61 7d :math:`X.=.\lambda(-ln(U))^{1/a}
58e00 60 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d `...........Parameters.........-
58e20 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 61 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 ---------.........a.:.float.or.a
58e40 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 rray_like.of.floats.............
58e60 53 68 61 70 65 20 70 61 72 61 6d 65 74 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 Shape.parameter.of.the.distribut
58e80 69 6f 6e 2e 20 20 4d 75 73 74 20 62 65 20 6e 6f 6e 6e 65 67 61 74 69 76 65 2e 0a 20 20 20 20 20 ion...Must.be.nonnegative.......
58ea0 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 ...size.:.int.or.tuple.of.ints,.
58ec0 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 optional.............Output.shap
58ee0 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c e...If.the.given.shape.is,.e.g.,
58f00 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 .``(m,.n,.k)``,.then............
58f20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e .``m.*.n.*.k``.samples.are.drawn
58f40 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 ...If.size.is.``None``.(default)
58f60 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 ,.............a.single.value.is.
58f80 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 61 60 60 20 69 73 20 61 20 73 63 61 6c 61 72 2e 20 20 returned.if.``a``.is.a.scalar...
58fa0 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6e 70 2e 61 72 72 61 Otherwise,.............``np.arra
58fc0 79 28 61 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a y(a).size``.samples.are.drawn...
58fe0 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a ........Returns.........-------.
59000 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a ........out.:.ndarray.or.scalar.
59020 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 ............Drawn.samples.from.t
59040 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 he.parameterized.Weibull.distrib
59060 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 ution...........See.Also........
59080 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 77 65 .--------.........scipy.stats.we
590a0 69 62 75 6c 6c 5f 6d 61 78 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 77 65 ibull_max.........scipy.stats.we
590c0 69 62 75 6c 6c 5f 6d 69 6e 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 67 65 ibull_min.........scipy.stats.ge
590e0 6e 65 78 74 72 65 6d 65 0a 20 20 20 20 20 20 20 20 67 75 6d 62 65 6c 0a 0a 20 20 20 20 20 20 20 nextreme.........gumbel.........
59100 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 .Notes.........-----.........The
59120 20 57 65 69 62 75 6c 6c 20 28 6f 72 20 54 79 70 65 20 49 49 49 20 61 73 79 6d 70 74 6f 74 69 63 .Weibull.(or.Type.III.asymptotic
59140 20 65 78 74 72 65 6d 65 20 76 61 6c 75 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 20 20 20 20 .extreme.value.distribution.....
59160 20 20 20 20 66 6f 72 20 73 6d 61 6c 6c 65 73 74 20 76 61 6c 75 65 73 2c 20 53 45 56 20 54 79 70 ....for.smallest.values,.SEV.Typ
59180 65 20 49 49 49 2c 20 6f 72 20 52 6f 73 69 6e 2d 52 61 6d 6d 6c 65 72 0a 20 20 20 20 20 20 20 20 e.III,.or.Rosin-Rammler.........
591a0 64 69 73 74 72 69 62 75 74 69 6f 6e 29 20 69 73 20 6f 6e 65 20 6f 66 20 61 20 63 6c 61 73 73 20 distribution).is.one.of.a.class.
591c0 6f 66 20 47 65 6e 65 72 61 6c 69 7a 65 64 20 45 78 74 72 65 6d 65 20 56 61 6c 75 65 0a 20 20 20 of.Generalized.Extreme.Value....
591e0 20 20 20 20 20 28 47 45 56 29 20 64 69 73 74 72 69 62 75 74 69 6f 6e 73 20 75 73 65 64 20 69 6e .....(GEV).distributions.used.in
59200 20 6d 6f 64 65 6c 69 6e 67 20 65 78 74 72 65 6d 65 20 76 61 6c 75 65 20 70 72 6f 62 6c 65 6d 73 .modeling.extreme.value.problems
59220 2e 0a 20 20 20 20 20 20 20 20 54 68 69 73 20 63 6c 61 73 73 20 69 6e 63 6c 75 64 65 73 20 74 68 ..........This.class.includes.th
59240 65 20 47 75 6d 62 65 6c 20 61 6e 64 20 46 72 65 63 68 65 74 20 64 69 73 74 72 69 62 75 74 69 6f e.Gumbel.and.Frechet.distributio
59260 6e 73 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e ns...........The.probability.den
59280 73 69 74 79 20 66 6f 72 20 74 68 65 20 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 75 74 69 6f sity.for.the.Weibull.distributio
592a0 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 5c n.is.............math::.p(x).=.\
592c0 66 72 61 63 7b 61 7d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 frac{a}.........................
592e0 20 7b 5c 6c 61 6d 62 64 61 7d 28 5c 66 72 61 63 7b 78 7d 7b 5c 6c 61 6d 62 64 61 7d 29 5e 7b 61 .{\lambda}(\frac{x}{\lambda})^{a
59300 2d 31 7d 65 5e 7b 2d 28 78 2f 5c 6c 61 6d 62 64 61 29 5e 61 7d 2c 0a 0a 20 20 20 20 20 20 20 20 -1}e^{-(x/\lambda)^a},..........
59320 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 61 60 20 69 73 20 74 68 65 20 73 68 61 70 65 20 61 6e 64 where.:math:`a`.is.the.shape.and
59340 20 3a 6d 61 74 68 3a 60 5c 6c 61 6d 62 64 61 60 20 74 68 65 20 73 63 61 6c 65 2e 0a 0a 20 20 20 .:math:`\lambda`.the.scale......
59360 20 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 20 68 61 73 20 69 74 73 20 70 65 61 6b 20 28 .....The.function.has.its.peak.(
59380 74 68 65 20 6d 6f 64 65 29 20 61 74 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 5c 6c 61 6d the.mode).at.........:math:`\lam
593a0 62 64 61 28 5c 66 72 61 63 7b 61 2d 31 7d 7b 61 7d 29 5e 7b 31 2f 61 7d 60 2e 0a 0a 20 20 20 20 bda(\frac{a-1}{a})^{1/a}`.......
593c0 20 20 20 20 57 68 65 6e 20 60 60 61 20 3d 20 31 60 60 2c 20 74 68 65 20 57 65 69 62 75 6c 6c 20 ....When.``a.=.1``,.the.Weibull.
593e0 64 69 73 74 72 69 62 75 74 69 6f 6e 20 72 65 64 75 63 65 73 20 74 6f 20 74 68 65 20 65 78 70 6f distribution.reduces.to.the.expo
59400 6e 65 6e 74 69 61 6c 0a 20 20 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 nential.........distribution....
59420 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d .......References.........------
59440 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 57 61 6c 6f 64 64 69 20 57 65 69 62 ----............[1].Waloddi.Weib
59460 75 6c 6c 2c 20 52 6f 79 61 6c 20 54 65 63 68 6e 69 63 61 6c 20 55 6e 69 76 65 72 73 69 74 79 2c ull,.Royal.Technical.University,
59480 20 53 74 6f 63 6b 68 6f 6c 6d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 31 39 33 39 20 .Stockholm,................1939.
594a0 22 41 20 53 74 61 74 69 73 74 69 63 61 6c 20 54 68 65 6f 72 79 20 4f 66 20 54 68 65 20 53 74 72 "A.Statistical.Theory.Of.The.Str
594c0 65 6e 67 74 68 20 4f 66 20 4d 61 74 65 72 69 61 6c 73 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 ength.Of.Materials",............
594e0 20 20 20 20 49 6e 67 65 6e 69 6f 72 73 76 65 74 65 6e 73 6b 61 70 73 61 6b 61 64 65 6d 69 65 6e ....Ingeniorsvetenskapsakademien
59500 73 20 48 61 6e 64 6c 69 6e 67 61 72 20 4e 72 20 31 35 31 2c 20 31 39 33 39 2c 0a 20 20 20 20 20 s.Handlingar.Nr.151,.1939,......
59520 20 20 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 6c 73 74 61 62 65 6e 73 20 4c 69 74 6f 67 72 61 ..........Generalstabens.Litogra
59540 66 69 73 6b 61 20 41 6e 73 74 61 6c 74 73 20 46 6f 72 6c 61 67 2c 20 53 74 6f 63 6b 68 6f 6c 6d fiska.Anstalts.Forlag,.Stockholm
59560 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 61 6c 6f 64 64 69 20 57 65 69 62 75 6c 6c .............[2].Waloddi.Weibull
59580 2c 20 22 41 20 53 74 61 74 69 73 74 69 63 61 6c 20 44 69 73 74 72 69 62 75 74 69 6f 6e 20 46 75 ,."A.Statistical.Distribution.Fu
595a0 6e 63 74 69 6f 6e 20 6f 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 57 69 64 65 20 41 70 nction.of................Wide.Ap
595c0 70 6c 69 63 61 62 69 6c 69 74 79 22 2c 20 4a 6f 75 72 6e 61 6c 20 4f 66 20 41 70 70 6c 69 65 64 plicability",.Journal.Of.Applied
595e0 20 4d 65 63 68 61 6e 69 63 73 20 41 53 4d 45 20 50 61 70 65 72 0a 20 20 20 20 20 20 20 20 20 20 .Mechanics.ASME.Paper...........
59600 20 20 20 20 20 31 39 35 31 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 33 5d 20 57 69 6b 69 70 65 .....1951.............[3].Wikipe
59620 64 69 61 2c 20 22 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 22 2c 0a 20 20 20 dia,."Weibull.distribution",....
59640 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 ............https://en.wikipedia
59660 2e 6f 72 67 2f 77 69 6b 69 2f 57 65 69 62 75 6c 6c 5f 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a .org/wiki/Weibull_distribution..
59680 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d ........Examples.........-------
596a0 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 -.........Draw.samples.from.the.
596c0 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 20 3d distribution:..........>>>.rng.=
596e0 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 20 20 20 20 20 20 .np.random.default_rng()........
59700 20 3e 3e 3e 20 61 20 3d 20 35 2e 20 23 20 73 68 61 70 65 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 .>>>.a.=.5..#.shape.........>>>.
59720 73 20 3d 20 72 6e 67 2e 77 65 69 62 75 6c 6c 28 61 2c 20 31 30 30 30 29 0a 0a 20 20 20 20 20 20 s.=.rng.weibull(a,.1000)........
59740 20 20 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 20 6f 66 20 74 68 65 20 73 ..Display.the.histogram.of.the.s
59760 61 6d 70 6c 65 73 2c 20 61 6c 6f 6e 67 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 74 68 65 20 70 amples,.along.with.........the.p
59780 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 3a 0a 0a 20 20 robability.density.function:....
597a0 20 20 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c ......>>>.import.matplotlib.pypl
597c0 6f 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 78 20 3d 20 6e 70 2e 61 72 61 ot.as.plt.........>>>.x.=.np.ara
597e0 6e 67 65 28 31 2c 31 30 30 2e 29 2f 35 30 2e 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 64 65 66 20 nge(1,100.)/50..........>>>.def.
59800 77 65 69 62 28 78 2c 6e 2c 61 29 3a 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 72 65 74 weib(x,n,a):.................ret
59820 75 72 6e 20 28 61 20 2f 20 6e 29 20 2a 20 28 78 20 2f 20 6e 29 2a 2a 28 61 20 2d 20 31 29 20 2a urn.(a./.n).*.(x./.n)**(a.-.1).*
59840 20 6e 70 2e 65 78 70 28 2d 28 78 20 2f 20 6e 29 2a 2a 61 29 0a 0a 20 20 20 20 20 20 20 20 3e 3e .np.exp(-(x./.n)**a)..........>>
59860 3e 20 63 6f 75 6e 74 2c 20 62 69 6e 73 2c 20 69 67 6e 6f 72 65 64 20 3d 20 70 6c 74 2e 68 69 73 >.count,.bins,.ignored.=.plt.his
59880 74 28 72 6e 67 2e 77 65 69 62 75 6c 6c 28 35 2e 2c 31 30 30 30 29 29 0a 20 20 20 20 20 20 20 20 t(rng.weibull(5.,1000)).........
598a0 3e 3e 3e 20 78 20 3d 20 6e 70 2e 61 72 61 6e 67 65 28 31 2c 31 30 30 2e 29 2f 35 30 2e 0a 20 20 >>>.x.=.np.arange(1,100.)/50....
598c0 20 20 20 20 20 20 3e 3e 3e 20 73 63 61 6c 65 20 3d 20 63 6f 75 6e 74 2e 6d 61 78 28 29 2f 77 65 ......>>>.scale.=.count.max()/we
598e0 69 62 28 78 2c 20 31 2e 2c 20 35 2e 29 2e 6d 61 78 28 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 ib(x,.1.,.5.).max().........>>>.
59900 70 6c 74 2e 70 6c 6f 74 28 78 2c 20 77 65 69 62 28 78 2c 20 31 2e 2c 20 35 2e 29 2a 73 63 61 6c plt.plot(x,.weib(x,.1.,.5.)*scal
59920 65 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 e).........>>>.plt.show().......
59940 20 20 20 00 64 66 00 00 49 6d 70 6f 72 74 45 72 72 6f 72 00 6b 61 70 70 61 00 00 00 00 00 00 00 ....df..ImportError.kappa.......
59960 0a 20 20 20 20 20 20 20 20 72 61 79 6c 65 69 67 68 28 73 63 61 6c 65 3d 31 2e 30 2c 20 73 69 7a .........rayleigh(scale=1.0,.siz
59980 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 e=None)..........Draw.samples.fr
599a0 6f 6d 20 61 20 52 61 79 6c 65 69 67 68 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 om.a.Rayleigh.distribution......
599c0 20 20 20 20 20 54 68 65 20 3a 6d 61 74 68 3a 60 5c 63 68 69 60 20 61 6e 64 20 57 65 69 62 75 6c .....The.:math:`\chi`.and.Weibul
599e0 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 73 20 61 72 65 20 67 65 6e 65 72 61 6c 69 7a 61 74 69 l.distributions.are.generalizati
59a00 6f 6e 73 20 6f 66 20 74 68 65 0a 20 20 20 20 20 20 20 20 52 61 79 6c 65 69 67 68 2e 0a 0a 20 20 ons.of.the.........Rayleigh.....
59a20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d ......Parameters.........-------
59a40 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 61 6c 65 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 ---.........scale.:.float.or.arr
59a60 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 ay_like.of.floats,.optional.....
59a80 20 20 20 20 20 20 20 20 53 63 61 6c 65 2c 20 61 6c 73 6f 20 65 71 75 61 6c 73 20 74 68 65 20 6d ........Scale,.also.equals.the.m
59aa0 6f 64 65 2e 20 4d 75 73 74 20 62 65 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 2e 20 44 65 66 61 75 ode..Must.be.non-negative..Defau
59ac0 6c 74 20 69 73 20 31 2e 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 lt.is.1..........size.:.int.or.t
59ae0 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 uple.of.ints,.optional..........
59b00 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 ...Output.shape...If.the.given.s
59b20 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 hape.is,.e.g.,.``(m,.n,.k)``,.th
59b40 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d en.............``m.*.n.*.k``.sam
59b60 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f ples.are.drawn...If.size.is.``No
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59ba0 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 73 63 61 6c ngle.value.is.returned.if.``scal
59bc0 65 60 60 20 69 73 20 61 20 73 63 61 6c 61 72 2e 20 20 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 e``.is.a.scalar...Otherwise,....
59be0 20 20 20 20 20 20 20 20 20 60 60 6e 70 2e 61 72 72 61 79 28 73 63 61 6c 65 29 2e 73 69 7a 65 60 .........``np.array(scale).size`
59c00 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 `.samples.are.drawn...........Re
59c20 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 turns.........-------.........ou
59c40 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 t.:.ndarray.or.scalar...........
59c60 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 ..Drawn.samples.from.the.paramet
59c80 65 72 69 7a 65 64 20 52 61 79 6c 65 69 67 68 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 erized.Rayleigh.distribution....
59ca0 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 .......Notes.........-----......
59cc0 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 ...The.probability.density.funct
59ce0 69 6f 6e 20 66 6f 72 20 74 68 65 20 52 61 79 6c 65 69 67 68 20 64 69 73 74 72 69 62 75 74 69 6f ion.for.the.Rayleigh.distributio
59d00 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 50 28 78 3b 73 63 61 6c n.is.............math::.P(x;scal
59d20 65 29 20 3d 20 5c 66 72 61 63 7b 78 7d 7b 73 63 61 6c 65 5e 32 7d 65 5e 7b 5c 66 72 61 63 7b 2d e).=.\frac{x}{scale^2}e^{\frac{-
59d40 78 5e 32 7d 7b 32 20 5c 63 64 6f 74 70 20 73 63 61 6c 65 5e 32 7d 7d 0a 0a 20 20 20 20 20 20 20 x^2}{2.\cdotp.scale^2}}.........
59d60 20 54 68 65 20 52 61 79 6c 65 69 67 68 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 77 6f 75 6c 64 .The.Rayleigh.distribution.would
59d80 20 61 72 69 73 65 2c 20 66 6f 72 20 65 78 61 6d 70 6c 65 2c 20 69 66 20 74 68 65 20 45 61 73 74 .arise,.for.example,.if.the.East
59da0 0a 20 20 20 20 20 20 20 20 61 6e 64 20 4e 6f 72 74 68 20 63 6f 6d 70 6f 6e 65 6e 74 73 20 6f 66 .........and.North.components.of
59dc0 20 74 68 65 20 77 69 6e 64 20 76 65 6c 6f 63 69 74 79 20 68 61 64 20 69 64 65 6e 74 69 63 61 6c .the.wind.velocity.had.identical
59de0 20 7a 65 72 6f 2d 6d 65 61 6e 0a 20 20 20 20 20 20 20 20 47 61 75 73 73 69 61 6e 20 64 69 73 74 .zero-mean.........Gaussian.dist
59e00 72 69 62 75 74 69 6f 6e 73 2e 20 20 54 68 65 6e 20 74 68 65 20 77 69 6e 64 20 73 70 65 65 64 20 ributions...Then.the.wind.speed.
59e20 77 6f 75 6c 64 20 68 61 76 65 20 61 20 52 61 79 6c 65 69 67 68 0a 20 20 20 20 20 20 20 20 64 69 would.have.a.Rayleigh.........di
59e40 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a stribution...........References.
59e60 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 ........----------............[1
59e80 5d 20 42 72 69 67 68 74 6f 6e 20 57 65 62 73 20 4c 74 64 2e 2c 20 22 52 61 79 6c 65 69 67 68 20 ].Brighton.Webs.Ltd.,."Rayleigh.
59ea0 44 69 73 74 72 69 62 75 74 69 6f 6e 2c 22 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 Distribution,"................ht
59ec0 74 70 73 3a 2f 2f 77 65 62 2e 61 72 63 68 69 76 65 2e 6f 72 67 2f 77 65 62 2f 32 30 30 39 30 35 tps://web.archive.org/web/200905
59ee0 31 34 30 39 31 34 32 34 2f 68 74 74 70 3a 2f 2f 62 72 69 67 68 74 6f 6e 2d 77 65 62 73 2e 63 6f 14091424/http://brighton-webs.co
59f00 2e 75 6b 3a 38 30 2f 64 69 73 74 72 69 62 75 74 69 6f 6e 73 2f 72 61 79 6c 65 69 67 68 2e 61 73 .uk:80/distributions/rayleigh.as
59f20 70 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 52 61 79 p............[2].Wikipedia,."Ray
59f40 6c 65 69 67 68 20 64 69 73 74 72 69 62 75 74 69 6f 6e 22 0a 20 20 20 20 20 20 20 20 20 20 20 20 leigh.distribution".............
59f60 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 ...https://en.wikipedia.org/wiki
59f80 2f 52 61 79 6c 65 69 67 68 5f 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 /Rayleigh_distribution..........
59fa0 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 Examples.........--------.......
59fc0 20 20 44 72 61 77 20 76 61 6c 75 65 73 20 66 72 6f 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 74 ..Draw.values.from.the.distribut
59fe0 69 6f 6e 20 61 6e 64 20 70 6c 6f 74 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 0a 0a 20 20 20 20 ion.and.plot.the.histogram......
5a000 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 69 ....>>>.from.matplotlib.pyplot.i
5a020 6d 70 6f 72 74 20 68 69 73 74 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 20 3d 20 6e 70 2e mport.hist.........>>>.rng.=.np.
5a040 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e random.default_rng().........>>>
5a060 20 76 61 6c 75 65 73 20 3d 20 68 69 73 74 28 72 6e 67 2e 72 61 79 6c 65 69 67 68 28 33 2c 20 31 .values.=.hist(rng.rayleigh(3,.1
5a080 30 30 30 30 30 29 2c 20 62 69 6e 73 3d 32 30 30 2c 20 64 65 6e 73 69 74 79 3d 54 72 75 65 29 0a 00000),.bins=200,.density=True).
5a0a0 0a 20 20 20 20 20 20 20 20 57 61 76 65 20 68 65 69 67 68 74 73 20 74 65 6e 64 20 74 6f 20 66 6f .........Wave.heights.tend.to.fo
5a0c0 6c 6c 6f 77 20 61 20 52 61 79 6c 65 69 67 68 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 49 66 llow.a.Rayleigh.distribution..If
5a0e0 20 74 68 65 20 6d 65 61 6e 20 77 61 76 65 0a 20 20 20 20 20 20 20 20 68 65 69 67 68 74 20 69 73 .the.mean.wave.........height.is
5a100 20 31 20 6d 65 74 65 72 2c 20 77 68 61 74 20 66 72 61 63 74 69 6f 6e 20 6f 66 20 77 61 76 65 73 .1.meter,.what.fraction.of.waves
5a120 20 61 72 65 20 6c 69 6b 65 6c 79 20 74 6f 20 62 65 20 6c 61 72 67 65 72 20 74 68 61 6e 20 33 0a .are.likely.to.be.larger.than.3.
5a140 20 20 20 20 20 20 20 20 6d 65 74 65 72 73 3f 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6d 65 61 ........meters?..........>>>.mea
5a160 6e 76 61 6c 75 65 20 3d 20 31 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6d 6f 64 65 76 61 6c 75 65 nvalue.=.1.........>>>.modevalue
5a180 20 3d 20 6e 70 2e 73 71 72 74 28 32 20 2f 20 6e 70 2e 70 69 29 20 2a 20 6d 65 61 6e 76 61 6c 75 .=.np.sqrt(2./.np.pi).*.meanvalu
5a1a0 65 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 72 6e 67 2e 72 61 79 6c 65 69 67 68 28 6d e.........>>>.s.=.rng.rayleigh(m
5a1c0 6f 64 65 76 61 6c 75 65 2c 20 31 30 30 30 30 30 30 29 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 odevalue,.1000000)..........The.
5a1e0 70 65 72 63 65 6e 74 61 67 65 20 6f 66 20 77 61 76 65 73 20 6c 61 72 67 65 72 20 74 68 61 6e 20 percentage.of.waves.larger.than.
5a200 33 20 6d 65 74 65 72 73 20 69 73 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 31 30 30 2e 2a 73 3.meters.is:..........>>>.100.*s
5a220 75 6d 28 73 3e 33 29 2f 31 30 30 30 30 30 30 2e 0a 20 20 20 20 20 20 20 20 30 2e 30 38 37 33 30 um(s>3)/1000000..........0.08730
5a240 30 30 30 30 30 30 30 30 30 30 30 30 33 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 0000000000003.#.random..........
5a260 00 00 00 00 61 6c 70 68 61 00 00 00 72 65 64 75 63 65 00 00 73 75 6d 00 3c 63 6f 6e 74 69 67 75 ....alpha...reduce..sum.<contigu
5a280 6f 75 73 20 61 6e 64 20 64 69 72 65 63 74 3e 00 65 6d 70 74 79 5f 6c 69 6b 65 00 00 4b 00 00 00 ous.and.direct>.empty_like..K...
5a2a0 55 6e 61 62 6c 65 20 74 6f 20 63 6f 6e 76 65 72 74 20 69 74 65 6d 20 74 6f 20 6f 62 6a 65 63 74 Unable.to.convert.item.to.object
5a2c0 00 00 00 00 70 76 61 6c 73 00 00 00 5f 70 63 67 36 34 00 00 6c 61 6d 00 72 65 73 68 61 70 65 00 ....pvals..._pcg64..lam.reshape.
5a2e0 68 61 73 6f 62 6a 65 63 74 00 00 00 65 6e 63 6f 64 65 00 00 54 00 00 00 47 65 6e 65 72 61 74 6f hasobject...encode..T...Generato
5a300 72 2e 62 69 6e 6f 6d 69 61 6c 20 28 6c 69 6e 65 20 32 38 30 37 29 00 00 5f 5f 65 6e 74 65 72 5f r.binomial.(line.2807)..__enter_
5a320 5f 00 00 00 65 69 67 68 00 00 00 00 69 73 6e 61 6e 00 00 00 6d 65 74 68 6f 64 00 00 6e 00 00 00 _...eigh....isnan...method..n...
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5a360 61 00 00 00 75 69 6e 74 36 34 00 00 70 00 00 00 62 69 74 5f 67 65 6e 65 72 61 74 6f 72 00 00 00 a...uint64..p...bit_generator...
5a380 47 65 6e 65 72 61 74 6f 72 2e 70 65 72 6d 75 74 65 64 20 28 6c 69 6e 65 20 34 33 32 36 29 00 00 Generator.permuted.(line.4326)..
5a3a0 73 61 66 65 00 00 00 00 45 6d 70 74 79 20 73 68 61 70 65 20 74 75 70 6c 65 20 66 6f 72 20 63 79 safe....Empty.shape.tuple.for.cy
5a3c0 74 68 6f 6e 2e 61 72 72 61 79 00 00 00 00 00 00 63 6f 6c 6f 72 73 20 6d 75 73 74 20 62 65 20 61 thon.array......colors.must.be.a
5a3e0 20 6f 6e 65 2d 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 73 65 71 75 65 6e 63 65 20 6f 66 20 6e 6f 6e .one-dimensional.sequence.of.non
5a400 6e 65 67 61 74 69 76 65 20 69 6e 74 65 67 65 72 73 20 6e 6f 74 20 65 78 63 65 65 64 69 6e 67 20 negative.integers.not.exceeding.
5a420 25 64 2e 00 73 71 72 74 00 00 00 00 00 00 00 00 49 6e 73 75 66 66 69 63 69 65 6e 74 20 6d 65 6d %d..sqrt........Insufficient.mem
5a440 6f 72 79 20 66 6f 72 20 6d 75 6c 74 69 76 61 72 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 ory.for.multivariate_hypergeomet
5a460 72 69 63 20 77 69 74 68 20 6d 65 74 68 6f 64 3d 27 63 6f 75 6e 74 27 20 61 6e 64 20 73 75 6d 28 ric.with.method='count'.and.sum(
5a480 63 6f 6c 6f 72 73 29 3d 25 64 00 00 61 6e 79 00 5f 5f 70 79 78 5f 72 65 73 75 6c 74 00 00 00 00 colors)=%d..any.__pyx_result....
5a4a0 6d 65 6d 76 69 65 77 00 53 65 71 75 65 6e 63 65 00 00 00 00 64 66 64 65 6e 00 00 00 70 69 63 6b memview.Sequence....dfden...pick
5a4c0 6c 65 00 00 78 00 00 00 65 6e 75 6d 65 72 61 74 65 00 00 00 75 69 6e 74 33 32 00 00 6d 75 00 00 le..x...enumerate...uint32..mu..
5a4e0 5f 5f 72 65 64 75 63 65 5f 63 79 74 68 6f 6e 5f 5f 00 00 00 63 6f 70 79 74 6f 00 00 6f 62 6a 00 __reduce_cython__...copyto..obj.
5a500 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 72 64 5f 74 20 28 6c 69 6e 65 20 31 36 38 37 29 Generator.standard_t.(line.1687)
5a520 00 00 00 00 69 6e 74 36 34 00 00 00 73 74 72 75 63 74 00 00 6d 61 78 00 61 73 61 72 72 61 79 00 ....int64...struct..max.asarray.
5a540 47 65 6e 65 72 61 74 6f 72 2e 6c 6f 67 69 73 74 69 63 20 28 6c 69 6e 65 20 32 33 37 38 29 00 00 Generator.logistic.(line.2378)..
5a560 0a 20 20 20 20 20 20 20 20 62 79 74 65 73 28 6c 65 6e 67 74 68 29 0a 0a 20 20 20 20 20 20 20 20 .........bytes(length)..........
5a580 52 65 74 75 72 6e 20 72 61 6e 64 6f 6d 20 62 79 74 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 Return.random.bytes...........Pa
5a5a0 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 rameters.........----------.....
5a5c0 20 20 20 20 6c 65 6e 67 74 68 20 3a 20 69 6e 74 0a 20 20 20 20 20 20 20 20 20 20 20 20 4e 75 6d ....length.:.int.............Num
5a5e0 62 65 72 20 6f 66 20 72 61 6e 64 6f 6d 20 62 79 74 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 ber.of.random.bytes...........Re
5a600 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 turns.........-------.........ou
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5a640 6c 65 6e 67 74 68 20 60 6c 65 6e 67 74 68 60 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c length.`length`...........Exampl
5a660 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 es.........--------.........>>>.
5a680 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 2e 62 79 74 65 73 28 31 30 np.random.default_rng().bytes(10
5a6a0 29 0a 20 20 20 20 20 20 20 20 62 27 5c 78 66 65 43 5c 78 39 62 5c 78 38 36 5c 78 31 37 5c 78 66 ).........b'\xfeC\x9b\x86\x17\xf
5a6c0 32 5c 78 61 31 5c 78 61 66 63 70 27 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 00 2\xa1\xafcp'.#.random...........
5a6e0 69 73 6e 61 74 69 76 65 00 00 00 00 73 68 61 70 65 00 00 00 2e 00 00 00 61 20 63 61 6e 6e 6f 74 isnative....shape.......a.cannot
5a700 20 62 65 20 65 6d 70 74 79 20 75 6e 6c 65 73 73 20 6e 6f 20 73 61 6d 70 6c 65 73 20 61 72 65 20 .be.empty.unless.no.samples.are.
5a720 74 61 6b 65 6e 00 00 00 6d 65 74 68 6f 64 20 6d 75 73 74 20 62 65 20 22 63 6f 75 6e 74 22 20 6f taken...method.must.be."count".o
5a740 72 20 22 6d 61 72 67 69 6e 61 6c 73 22 2e 00 00 0a 20 20 20 20 20 20 20 20 6e 65 67 61 74 69 76 r."marginals"............negativ
5a760 65 5f 62 69 6e 6f 6d 69 61 6c 28 6e 2c 20 70 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 e_binomial(n,.p,.size=None).....
5a780 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 6e 65 67 61 74 69 76 .....Draw.samples.from.a.negativ
5a7a0 65 20 62 69 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 e.binomial.distribution.........
5a7c0 20 20 53 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 20 66 72 6f 6d 20 61 20 6e 65 67 61 74 ..Samples.are.drawn.from.a.negat
5a7e0 69 76 65 20 62 69 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 77 69 74 68 20 73 ive.binomial.distribution.with.s
5a800 70 65 63 69 66 69 65 64 0a 20 20 20 20 20 20 20 20 70 61 72 61 6d 65 74 65 72 73 2c 20 60 6e 60 pecified.........parameters,.`n`
5a820 20 73 75 63 63 65 73 73 65 73 20 61 6e 64 20 60 70 60 20 70 72 6f 62 61 62 69 6c 69 74 79 20 6f .successes.and.`p`.probability.o
5a840 66 20 73 75 63 63 65 73 73 20 77 68 65 72 65 20 60 6e 60 0a 20 20 20 20 20 20 20 20 69 73 20 3e f.success.where.`n`.........is.>
5a860 20 30 20 61 6e 64 20 60 70 60 20 69 73 20 69 6e 20 74 68 65 20 69 6e 74 65 72 76 61 6c 20 28 30 .0.and.`p`.is.in.the.interval.(0
5a880 2c 20 31 5d 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 ,.1]...........Parameters.......
5a8a0 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6e 20 3a 20 66 6c 6f 61 74 20 6f ..----------.........n.:.float.o
5a8c0 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 r.array_like.of.floats..........
5a8e0 20 20 20 50 61 72 61 6d 65 74 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e ...Parameter.of.the.distribution
5a900 2c 20 3e 20 30 2e 0a 20 20 20 20 20 20 20 20 70 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 ,.>.0..........p.:.float.or.arra
5a920 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 50 61 72 y_like.of.floats.............Par
5a940 61 6d 65 74 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 4d 75 73 74 ameter.of.the.distribution..Must
5a960 20 73 61 74 69 73 66 79 20 30 20 3c 20 70 20 3c 3d 20 31 2e 0a 20 20 20 20 20 20 20 20 73 69 7a .satisfy.0.<.p.<=.1..........siz
5a980 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e e.:.int.or.tuple.of.ints,.option
5a9a0 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 al.............Output.shape...If
5a9c0 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c .the.given.shape.is,.e.g.,.``(m,
5a9e0 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a .n,.k)``,.then.............``m.*
5aa00 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 20 .n.*.k``.samples.are.drawn...If.
5aa20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 20 size.is.``None``.(default),.....
5aa40 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e ........a.single.value.is.return
5aa60 65 64 20 69 66 20 60 60 6e 60 60 20 61 6e 64 20 60 60 70 60 60 20 61 72 65 20 62 6f 74 68 20 73 ed.if.``n``.and.``p``.are.both.s
5aa80 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 68 65 72 77 69 73 65 2c 20 60 calars..............Otherwise,.`
5aaa0 60 6e 70 2e 62 72 6f 61 64 63 61 73 74 28 6e 2c 20 70 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c `np.broadcast(n,.p).size``.sampl
5aac0 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 es.are.drawn...........Returns..
5aae0 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 .......-------.........out.:.nda
5ab00 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e rray.or.scalar.............Drawn
5ab20 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 .samples.from.the.parameterized.
5ab40 6e 65 67 61 74 69 76 65 20 62 69 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 0a negative.binomial.distribution,.
5ab60 20 20 20 20 20 20 20 20 20 20 20 20 77 68 65 72 65 20 65 61 63 68 20 73 61 6d 70 6c 65 20 69 73 ............where.each.sample.is
5ab80 20 65 71 75 61 6c 20 74 6f 20 4e 2c 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 66 61 69 6c 75 .equal.to.N,.the.number.of.failu
5aba0 72 65 73 20 74 68 61 74 0a 20 20 20 20 20 20 20 20 20 20 20 20 6f 63 63 75 72 72 65 64 20 62 65 res.that.............occurred.be
5abc0 66 6f 72 65 20 61 20 74 6f 74 61 6c 20 6f 66 20 6e 20 73 75 63 63 65 73 73 65 73 20 77 61 73 20 fore.a.total.of.n.successes.was.
5abe0 72 65 61 63 68 65 64 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 reached...........Notes.........
5ac00 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 6d 61 -----.........The.probability.ma
5ac20 73 73 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 74 68 65 20 6e 65 67 61 74 69 76 65 20 62 69 6e 6f ss.function.of.the.negative.bino
5ac40 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e mial.distribution.is............
5ac60 20 6d 61 74 68 3a 3a 20 50 28 4e 3b 6e 2c 70 29 20 3d 20 5c 66 72 61 63 7b 5c 47 61 6d 6d 61 28 .math::.P(N;n,p).=.\frac{\Gamma(
5ac80 4e 2b 6e 29 7d 7b 4e 21 5c 47 61 6d 6d 61 28 6e 29 7d 70 5e 7b 6e 7d 28 31 2d 70 29 5e 7b 4e 7d N+n)}{N!\Gamma(n)}p^{n}(1-p)^{N}
5aca0 2c 0a 0a 20 20 20 20 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 6e 60 20 69 73 20 74 68 ,..........where.:math:`n`.is.th
5acc0 65 20 6e 75 6d 62 65 72 20 6f 66 20 73 75 63 63 65 73 73 65 73 2c 20 3a 6d 61 74 68 3a 60 70 60 e.number.of.successes,.:math:`p`
5ace0 20 69 73 20 74 68 65 0a 20 20 20 20 20 20 20 20 70 72 6f 62 61 62 69 6c 69 74 79 20 6f 66 20 73 .is.the.........probability.of.s
5ad00 75 63 63 65 73 73 2c 20 3a 6d 61 74 68 3a 60 4e 2b 6e 60 20 69 73 20 74 68 65 20 6e 75 6d 62 65 uccess,.:math:`N+n`.is.the.numbe
5ad20 72 20 6f 66 20 74 72 69 61 6c 73 2c 20 61 6e 64 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 r.of.trials,.and.........:math:`
5ad40 5c 47 61 6d 6d 61 60 20 69 73 20 74 68 65 20 67 61 6d 6d 61 20 66 75 6e 63 74 69 6f 6e 2e 20 57 \Gamma`.is.the.gamma.function..W
5ad60 68 65 6e 20 3a 6d 61 74 68 3a 60 6e 60 20 69 73 20 61 6e 20 69 6e 74 65 67 65 72 2c 0a 20 20 20 hen.:math:`n`.is.an.integer,....
5ad80 20 20 20 20 20 3a 6d 61 74 68 3a 60 5c 66 72 61 63 7b 5c 47 61 6d 6d 61 28 4e 2b 6e 29 7d 7b 4e .....:math:`\frac{\Gamma(N+n)}{N
5ada0 21 5c 47 61 6d 6d 61 28 6e 29 7d 20 3d 20 5c 62 69 6e 6f 6d 7b 4e 2b 6e 2d 31 7d 7b 4e 7d 60 2c !\Gamma(n)}.=.\binom{N+n-1}{N}`,
5adc0 20 77 68 69 63 68 20 69 73 0a 20 20 20 20 20 20 20 20 74 68 65 20 6d 6f 72 65 20 63 6f 6d 6d 6f .which.is.........the.more.commo
5ade0 6e 20 66 6f 72 6d 20 6f 66 20 74 68 69 73 20 74 65 72 6d 20 69 6e 20 74 68 65 20 74 68 65 20 70 n.form.of.this.term.in.the.the.p
5ae00 6d 66 2e 20 54 68 65 20 6e 65 67 61 74 69 76 65 0a 20 20 20 20 20 20 20 20 62 69 6e 6f 6d 69 61 mf..The.negative.........binomia
5ae20 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 67 69 76 65 73 20 74 68 65 20 70 72 6f 62 61 62 69 l.distribution.gives.the.probabi
5ae40 6c 69 74 79 20 6f 66 20 4e 20 66 61 69 6c 75 72 65 73 20 67 69 76 65 6e 20 6e 0a 20 20 20 20 20 lity.of.N.failures.given.n......
5ae60 20 20 20 73 75 63 63 65 73 73 65 73 2c 20 77 69 74 68 20 61 20 73 75 63 63 65 73 73 20 6f 6e 20 ...successes,.with.a.success.on.
5ae80 74 68 65 20 6c 61 73 74 20 74 72 69 61 6c 2e 0a 0a 20 20 20 20 20 20 20 20 49 66 20 6f 6e 65 20 the.last.trial...........If.one.
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5c140 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 4e 75 6d 62 65 72 20 6f 66 20 64 65 floats..............Number.of.de
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5c220 72 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 rawn...If.size.is.``None``.(defa
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5c4a0 5f 7b 69 3d 30 7d 5e 7b 5c 6d 61 74 68 74 74 7b 64 66 7d 7d 20 58 5e 32 5f 69 0a 0a 20 20 20 20 _{i=0}^{\mathtt{df}}.X^2_i......
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5c500 20 5c 63 68 69 5e 32 5f 6b 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c .\chi^2_k...........The.probabil
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5c5e0 73 20 74 68 65 20 67 61 6d 6d 61 20 66 75 6e 63 74 69 6f 6e 2c 0a 0a 20 20 20 20 20 20 20 20 2e s.the.gamma.function,...........
5c600 2e 20 6d 61 74 68 3a 3a 20 5c 47 61 6d 6d 61 28 78 29 20 3d 20 5c 69 6e 74 5f 30 5e 7b 2d 5c 69 ..math::.\Gamma(x).=.\int_0^{-\i
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5c640 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d ....References.........---------
5c660 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 4e 49 53 54 20 22 45 6e 67 69 6e 65 65 72 69 -............[1].NIST."Engineeri
5c680 6e 67 20 53 74 61 74 69 73 74 69 63 73 20 48 61 6e 64 62 6f 6f 6b 22 0a 20 20 20 20 20 20 20 20 ng.Statistics.Handbook".........
5c6a0 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 77 77 77 2e 69 74 6c 2e 6e 69 73 74 2e 67 6f 76 2f .......https://www.itl.nist.gov/
5c6c0 64 69 76 38 39 38 2f 68 61 6e 64 62 6f 6f 6b 2f 65 64 61 2f 73 65 63 74 69 6f 6e 33 2f 65 64 61 div898/handbook/eda/section3/eda
5c6e0 33 36 36 36 2e 68 74 6d 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 3666.htm..........Examples......
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5c720 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 2e 63 68 69 73 71 75 61 72 65 28 32 2c 34 29 0a 20 m.default_rng().chisquare(2,4)..
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5c7a0 0a 20 20 20 20 20 20 20 20 67 75 6d 62 65 6c 28 6c 6f 63 3d 30 2e 30 2c 20 73 63 61 6c 65 3d 31 .........gumbel(loc=0.0,.scale=1
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5c800 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 47 75 ..........Draw.samples.from.a.Gu
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5c8c0 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 Parameters.........----------...
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5c900 6f 66 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 of.floats,.optional.............
5c920 54 68 65 20 6c 6f 63 61 74 69 6f 6e 20 6f 66 20 74 68 65 20 6d 6f 64 65 20 6f 66 20 74 68 65 20 The.location.of.the.mode.of.the.
5c940 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 44 65 66 61 75 6c 74 20 69 73 20 30 2e 0a 20 20 20 20 distribution..Default.is.0......
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5c980 6f 66 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 of.floats,.optional.............
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5d2c0 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 47 75 6d 62 65 6c 2c 20 45 2e 20 -----............[1].Gumbel,.E..
5d2e0 4a 2e 2c 20 22 53 74 61 74 69 73 74 69 63 73 20 6f 66 20 45 78 74 72 65 6d 65 73 2c 22 0a 20 20 J.,."Statistics.of.Extremes,"...
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5d320 55 6e 69 76 65 72 73 69 74 79 20 50 72 65 73 73 2c 20 31 39 35 38 2e 0a 20 20 20 20 20 20 20 20 University.Press,.1958..........
5d340 2e 2e 20 5b 32 5d 20 52 65 69 73 73 2c 20 52 2e 2d 44 2e 20 61 6e 64 20 54 68 6f 6d 61 73 2c 20 ...[2].Reiss,.R.-D..and.Thomas,.
5d360 4d 2e 2c 20 22 53 74 61 74 69 73 74 69 63 61 6c 20 41 6e 61 6c 79 73 69 73 20 6f 66 20 45 78 74 M.,."Statistical.Analysis.of.Ext
5d380 72 65 6d 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 56 61 6c 75 65 73 20 66 72 6f 6d 20 reme................Values.from.
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5d4c0 2e 67 75 6d 62 65 6c 28 6d 75 2c 20 62 65 74 61 2c 20 31 30 30 30 29 0a 0a 20 20 20 20 20 20 20 .gumbel(mu,.beta,.1000).........
5d4e0 20 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 20 6f 66 20 74 68 65 20 73 61 .Display.the.histogram.of.the.sa
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5d520 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 3a 0a 0a 20 20 20 obability.density.function:.....
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5d820 28 36 29 20 2f 20 6e 70 2e 70 69 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6d 75 20 3d 20 6e 70 2e (6)./.np.pi.........>>>.mu.=.np.
5d840 6d 65 61 6e 28 6d 61 78 69 6d 61 29 20 2d 20 30 2e 35 37 37 32 31 2a 62 65 74 61 0a 20 20 20 20 mean(maxima).-.0.57721*beta.....
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5e2c0 20 20 20 20 20 20 20 20 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 65 73 6f 75 72 63 65 2e 0a 20 .........Wolfram.Web.Resource...
5e2e0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d 61 74 68 77 6f 72 6c 64 2e 77 ..............http://mathworld.w
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5e320 6c 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 47 61 6d l............[2].Wikipedia,."Gam
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5ee40 54 6f 20 73 68 75 66 66 6c 65 20 74 68 65 20 72 6f 77 73 20 6f 66 20 60 78 60 20 69 6e 2d 70 6c To.shuffle.the.rows.of.`x`.in-pl
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5efe0 20 20 20 54 72 75 65 0a 20 20 20 20 20 20 20 20 00 00 00 00 72 74 6f 6c 00 00 00 00 00 00 00 00 ...True.............rtol........
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5f060 20 20 20 20 20 20 53 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 20 66 72 6f 6d 20 61 20 76 ......Samples.are.drawn.from.a.v
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5f1e0 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d ........Parameters.........-----
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5f220 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 4d 6f 64 y_like.of.floats.............Mod
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5f260 2e 0a 20 20 20 20 20 20 20 20 6b 61 70 70 61 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 ..........kappa.:.float.or.array
5f280 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 69 73 70 _like.of.floats.............Disp
5f2a0 65 72 73 69 6f 6e 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 20 68 61 73 20 ersion.of.the.distribution,.has.
5f2c0 74 6f 20 62 65 20 3e 3d 30 2e 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 to.be.>=0..........size.:.int.or
5f2e0 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 .tuple.of.ints,.optional........
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5f340 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 then.............``m.*.n.*.k``.s
5f360 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 amples.are.drawn...If.size.is.``
5f380 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 None``.(default),.............a.
5f3a0 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 6d 75 single.value.is.returned.if.``mu
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5f3e0 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 68 65 72 77 69 73 65 2c 20 60 60 6e 70 2e 62 s..............Otherwise,.``np.b
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5f420 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 es.are.drawn...........Returns..
5f440 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 .......-------.........out.:.nda
5f460 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e rray.or.scalar.............Drawn
5f480 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 .samples.from.the.parameterized.
5f4a0 76 6f 6e 20 4d 69 73 65 73 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 von.Mises.distribution..........
5f4c0 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 .See.Also.........--------......
5f4e0 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 76 6f 6e 6d 69 73 65 73 20 3a 20 70 72 6f 62 61 62 ...scipy.stats.vonmises.:.probab
5f500 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 64 69 73 74 72 69 62 75 ility.density.function,.distribu
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5f540 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 65 74 63 2e 0a 0a 20 20 20 20 20 20 20 20 density.function,.etc...........
5f560 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 Notes.........-----.........The.
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5fa20 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 20 6f 66 20 74 68 65 20 73 61 6d Display.the.histogram.of.the.sam
5fa40 70 6c 65 73 2c 20 61 6c 6f 6e 67 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 74 68 65 20 70 72 6f ples,.along.with.........the.pro
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5fb60 63 6f 73 28 78 2d 6d 75 29 29 2f 28 32 2a 6e 70 2e 70 69 2a 69 30 28 6b 61 70 70 61 29 29 20 20 cos(x-mu))/(2*np.pi*i0(kappa))..
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5fc20 68 61 70 65 2c 20 73 63 61 6c 65 3d 31 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 hape,.scale=1.0,.size=None).....
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5fd40 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d ....Parameters.........---------
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5fde0 63 61 6c 65 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c cale.:.float.or.array_like.of.fl
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60380 20 20 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 65 73 6f 75 72 63 65 2e 0a 20 20 20 20 20 20 20 ...Wolfram.Web.Resource.........
603a0 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d 61 74 68 77 6f 72 6c 64 2e 77 6f 6c 66 72 61 6d ........http://mathworld.wolfram
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603e0 20 20 20 20 2e 2e 20 5b 32 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 47 61 6d 6d 61 20 64 69 73 .......[2].Wikipedia,."Gamma.dis
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60720 47 65 6e 65 72 61 74 6f 72 2e 70 6f 77 65 72 20 28 6c 69 6e 65 20 32 30 37 33 29 00 00 00 00 00 Generator.power.(line.2073).....
60740 63 61 70 73 75 6c 65 00 6d 6f 64 65 00 00 00 00 57 68 65 6e 20 6d 65 74 68 6f 64 20 69 73 20 27 capsule.mode....When.method.is.'
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61900 53 54 2f 53 45 4d 41 54 45 43 48 20 65 2d 48 61 6e 64 62 6f 6f 6b 20 6f 66 20 53 74 61 74 69 73 ST/SEMATECH.e-Handbook.of.Statis
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61960 20 20 68 74 74 70 73 3a 2f 2f 77 77 77 2e 69 74 6c 2e 6e 69 73 74 2e 67 6f 76 2f 64 69 76 38 39 ..https://www.itl.nist.gov/div89
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62be0 68 6f 77 28 29 0a 0a 20 20 20 20 20 20 20 20 00 0a 20 20 20 20 20 20 20 20 66 28 64 66 6e 75 6d how()....................f(dfnum
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62c40 2e 0a 0a 20 20 20 20 20 20 20 20 53 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 20 66 72 6f ...........Samples.are.drawn.fro
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62cc0 20 61 6e 64 20 60 64 66 64 65 6e 60 20 28 64 65 67 72 65 65 73 20 6f 66 0a 20 20 20 20 20 20 20 .and.`dfden`.(degrees.of........
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62d00 62 6f 74 68 20 70 61 72 61 6d 65 74 65 72 73 20 6d 75 73 74 20 62 65 20 67 72 65 61 74 65 72 20 both.parameters.must.be.greater.
62d20 74 68 61 6e 0a 20 20 20 20 20 20 20 20 7a 65 72 6f 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 than.........zero...........The.
62d40 72 61 6e 64 6f 6d 20 76 61 72 69 61 74 65 20 6f 66 20 74 68 65 20 46 20 64 69 73 74 72 69 62 75 random.variate.of.the.F.distribu
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62de0 2c 20 61 6e 64 20 69 73 20 74 68 65 20 72 61 74 69 6f 20 6f 66 20 74 77 6f 20 63 68 69 2d 73 71 ,.and.is.the.ratio.of.two.chi-sq
62e00 75 61 72 65 0a 20 20 20 20 20 20 20 20 76 61 72 69 61 74 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 uare.........variates...........
62e20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 Parameters.........----------...
62e40 20 20 20 20 20 20 64 66 6e 75 6d 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b ......dfnum.:.float.or.array_lik
62e60 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 65 67 72 65 65 73 20 e.of.floats.............Degrees.
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62fc0 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 20 20 20 20 20 20 20 s.``None``.(default),...........
62fe0 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 66 20 ..a.single.value.is.returned.if.
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63020 20 73 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 68 65 72 77 69 73 65 2c .scalars..............Otherwise,
63040 20 60 60 6e 70 2e 62 72 6f 61 64 63 61 73 74 28 64 66 6e 75 6d 2c 20 64 66 64 65 6e 29 2e 73 69 .``np.broadcast(dfnum,.dfden).si
63060 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 ze``.samples.are.drawn..........
63080 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 .Returns.........-------........
630a0 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 .out.:.ndarray.or.scalar........
630c0 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 .....Drawn.samples.from.the.para
630e0 6d 65 74 65 72 69 7a 65 64 20 46 69 73 68 65 72 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a meterized.Fisher.distribution...
63100 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d ........See.Also.........-------
63120 2d 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 66 20 3a 20 70 72 6f 62 61 62 -.........scipy.stats.f.:.probab
63140 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 64 69 73 74 72 69 62 75 ility.density.function,.distribu
63160 74 69 6f 6e 20 6f 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 63 75 6d 75 6c 61 74 69 76 65 20 64 tion.or.............cumulative.d
63180 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 65 74 63 2e 0a 0a 20 20 20 20 20 20 20 20 4e ensity.function,.etc...........N
631a0 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 46 otes.........-----.........The.F
631c0 20 73 74 61 74 69 73 74 69 63 20 69 73 20 75 73 65 64 20 74 6f 20 63 6f 6d 70 61 72 65 20 69 6e .statistic.is.used.to.compare.in
631e0 2d 67 72 6f 75 70 20 76 61 72 69 61 6e 63 65 73 20 74 6f 20 62 65 74 77 65 65 6e 2d 67 72 6f 75 -group.variances.to.between-grou
63200 70 0a 20 20 20 20 20 20 20 20 76 61 72 69 61 6e 63 65 73 2e 20 43 61 6c 63 75 6c 61 74 69 6e 67 p.........variances..Calculating
63220 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 64 65 70 65 6e 64 73 20 6f 6e 20 74 68 65 .the.distribution.depends.on.the
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63260 61 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 74 68 65 20 72 65 73 70 65 63 74 69 76 65 20 64 65 67 a.function.of.the.respective.deg
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632a0 72 6f 62 6c 65 6d 2e 20 20 54 68 65 20 76 61 72 69 61 62 6c 65 20 60 64 66 6e 75 6d 60 20 69 73 roblem...The.variable.`dfnum`.is
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632e0 2c 20 74 68 65 0a 20 20 20 20 20 20 20 20 62 65 74 77 65 65 6e 2d 67 72 6f 75 70 73 20 64 65 67 ,.the.........between-groups.deg
63300 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 2c 20 77 68 69 6c 65 20 60 64 66 64 65 6e 60 20 69 rees.of.freedom,.while.`dfden`.i
63320 73 20 74 68 65 20 77 69 74 68 69 6e 2d 67 72 6f 75 70 73 0a 20 20 20 20 20 20 20 20 64 65 67 72 s.the.within-groups.........degr
63340 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 2c 20 74 68 65 20 73 75 6d 20 6f 66 20 74 68 65 20 6e ees.of.freedom,.the.sum.of.the.n
63360 75 6d 62 65 72 20 6f 66 20 73 61 6d 70 6c 65 73 20 69 6e 20 65 61 63 68 20 67 72 6f 75 70 0a 20 umber.of.samples.in.each.group..
63380 20 20 20 20 20 20 20 6d 69 6e 75 73 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 67 72 6f 75 70 .......minus.the.number.of.group
633a0 73 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d s...........References.........-
633c0 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 47 6c 61 6e 74 7a 2c ---------............[1].Glantz,
633e0 20 53 74 61 6e 74 6f 6e 20 41 2e 20 22 50 72 69 6d 65 72 20 6f 66 20 42 69 6f 73 74 61 74 69 73 .Stanton.A.."Primer.of.Biostatis
63400 74 69 63 73 2e 22 2c 20 4d 63 47 72 61 77 2d 48 69 6c 6c 2c 0a 20 20 20 20 20 20 20 20 20 20 20 tics.",.McGraw-Hill,............
63420 20 20 20 20 46 69 66 74 68 20 45 64 69 74 69 6f 6e 2c 20 32 30 30 32 2e 0a 20 20 20 20 20 20 20 ....Fifth.Edition,.2002.........
63440 20 2e 2e 20 5b 32 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 46 2d 64 69 73 74 72 69 62 75 74 69 ....[2].Wikipedia,."F-distributi
63460 6f 6e 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 on",................https://en.w
63480 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 46 2d 64 69 73 74 72 69 62 75 74 69 6f 6e ikipedia.org/wiki/F-distribution
634a0 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d ..........Examples.........-----
634c0 2d 2d 2d 0a 20 20 20 20 20 20 20 20 41 6e 20 65 78 61 6d 70 6c 65 20 66 72 6f 6d 20 47 6c 61 6e ---.........An.example.from.Glan
634e0 74 7a 5b 31 5d 2c 20 70 70 20 34 37 2d 34 30 3a 0a 0a 20 20 20 20 20 20 20 20 54 77 6f 20 67 72 tz[1],.pp.47-40:..........Two.gr
63500 6f 75 70 73 2c 20 63 68 69 6c 64 72 65 6e 20 6f 66 20 64 69 61 62 65 74 69 63 73 20 28 32 35 20 oups,.children.of.diabetics.(25.
63520 70 65 6f 70 6c 65 29 20 61 6e 64 20 63 68 69 6c 64 72 65 6e 20 66 72 6f 6d 20 70 65 6f 70 6c 65 people).and.children.from.people
63540 0a 20 20 20 20 20 20 20 20 77 69 74 68 6f 75 74 20 64 69 61 62 65 74 65 73 20 28 32 35 20 63 6f .........without.diabetes.(25.co
63560 6e 74 72 6f 6c 73 29 2e 20 46 61 73 74 69 6e 67 20 62 6c 6f 6f 64 20 67 6c 75 63 6f 73 65 20 77 ntrols)..Fasting.blood.glucose.w
63580 61 73 20 6d 65 61 73 75 72 65 64 2c 0a 20 20 20 20 20 20 20 20 63 61 73 65 20 67 72 6f 75 70 20 as.measured,.........case.group.
635a0 68 61 64 20 61 20 6d 65 61 6e 20 76 61 6c 75 65 20 6f 66 20 38 36 2e 31 2c 20 63 6f 6e 74 72 6f had.a.mean.value.of.86.1,.contro
635c0 6c 73 20 68 61 64 20 61 20 6d 65 61 6e 20 76 61 6c 75 65 20 6f 66 0a 20 20 20 20 20 20 20 20 38 ls.had.a.mean.value.of.........8
635e0 32 2e 32 2e 20 53 74 61 6e 64 61 72 64 20 64 65 76 69 61 74 69 6f 6e 73 20 77 65 72 65 20 32 2e 2.2..Standard.deviations.were.2.
63600 30 39 20 61 6e 64 20 32 2e 34 39 20 72 65 73 70 65 63 74 69 76 65 6c 79 2e 20 41 72 65 20 74 68 09.and.2.49.respectively..Are.th
63620 65 73 65 0a 20 20 20 20 20 20 20 20 64 61 74 61 20 63 6f 6e 73 69 73 74 65 6e 74 20 77 69 74 68 ese.........data.consistent.with
63640 20 74 68 65 20 6e 75 6c 6c 20 68 79 70 6f 74 68 65 73 69 73 20 74 68 61 74 20 74 68 65 20 70 61 .the.null.hypothesis.that.the.pa
63660 72 65 6e 74 73 20 64 69 61 62 65 74 69 63 0a 20 20 20 20 20 20 20 20 73 74 61 74 75 73 20 64 6f rents.diabetic.........status.do
63680 65 73 20 6e 6f 74 20 61 66 66 65 63 74 20 74 68 65 69 72 20 63 68 69 6c 64 72 65 6e 27 73 20 62 es.not.affect.their.children's.b
636a0 6c 6f 6f 64 20 67 6c 75 63 6f 73 65 20 6c 65 76 65 6c 73 3f 0a 20 20 20 20 20 20 20 20 43 61 6c lood.glucose.levels?.........Cal
636c0 63 75 6c 61 74 69 6e 67 20 74 68 65 20 46 20 73 74 61 74 69 73 74 69 63 20 66 72 6f 6d 20 74 68 culating.the.F.statistic.from.th
636e0 65 20 64 61 74 61 20 67 69 76 65 73 20 61 20 76 61 6c 75 65 20 6f 66 20 33 36 2e 30 31 2e 0a 0a e.data.gives.a.value.of.36.01...
63700 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 64 69 ........Draw.samples.from.the.di
63720 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 64 66 6e 75 6d 20 3d stribution:..........>>>.dfnum.=
63740 20 31 2e 20 23 20 62 65 74 77 65 65 6e 20 67 72 6f 75 70 20 64 65 67 72 65 65 73 20 6f 66 20 66 .1..#.between.group.degrees.of.f
63760 72 65 65 64 6f 6d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 64 66 64 65 6e 20 3d 20 34 38 2e 20 23 reedom.........>>>.dfden.=.48..#
63780 20 77 69 74 68 69 6e 20 67 72 6f 75 70 73 20 64 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f .within.groups.degrees.of.freedo
637a0 6d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 m.........>>>.s.=.np.random.defa
637c0 75 6c 74 5f 72 6e 67 28 29 2e 66 28 64 66 6e 75 6d 2c 20 64 66 64 65 6e 2c 20 31 30 30 30 29 0a ult_rng().f(dfnum,.dfden,.1000).
637e0 0a 20 20 20 20 20 20 20 20 54 68 65 20 6c 6f 77 65 72 20 62 6f 75 6e 64 20 66 6f 72 20 74 68 65 .........The.lower.bound.for.the
63800 20 74 6f 70 20 31 25 20 6f 66 20 74 68 65 20 73 61 6d 70 6c 65 73 20 69 73 20 3a 0a 0a 20 20 20 .top.1%.of.the.samples.is.:.....
63820 20 20 20 20 20 3e 3e 3e 20 6e 70 2e 73 6f 72 74 28 73 29 5b 2d 31 30 5d 0a 20 20 20 20 20 20 20 .....>>>.np.sort(s)[-10]........
63840 20 37 2e 36 31 39 38 38 31 32 30 39 38 35 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 .7.61988120985.#.random.........
63860 20 53 6f 20 74 68 65 72 65 20 69 73 20 61 62 6f 75 74 20 61 20 31 25 20 63 68 61 6e 63 65 20 74 .So.there.is.about.a.1%.chance.t
63880 68 61 74 20 74 68 65 20 46 20 73 74 61 74 69 73 74 69 63 20 77 69 6c 6c 20 65 78 63 65 65 64 20 hat.the.F.statistic.will.exceed.
638a0 37 2e 36 32 2c 0a 20 20 20 20 20 20 20 20 74 68 65 20 6d 65 61 73 75 72 65 64 20 76 61 6c 75 65 7.62,.........the.measured.value
638c0 20 69 73 20 33 36 2c 20 73 6f 20 74 68 65 20 6e 75 6c 6c 20 68 79 70 6f 74 68 65 73 69 73 20 69 .is.36,.so.the.null.hypothesis.i
638e0 73 20 72 65 6a 65 63 74 65 64 20 61 74 20 74 68 65 20 31 25 0a 20 20 20 20 20 20 20 20 6c 65 76 s.rejected.at.the.1%.........lev
63900 65 6c 2e 0a 0a 20 20 20 20 20 20 20 20 00 00 00 5f 5f 72 65 64 75 63 65 5f 5f 00 00 00 00 00 00 el..............__reduce__......
63920 63 6f 76 61 72 69 61 6e 63 65 20 69 73 20 6e 6f 74 20 70 6f 73 69 74 69 76 65 2d 73 65 6d 69 64 covariance.is.not.positive-semid
63940 65 66 69 6e 69 74 65 2e 00 00 00 00 61 78 69 73 00 00 00 00 00 00 00 00 5f 5f 6e 65 77 5f 5f 00 efinite.....axis........__new__.
63960 43 61 6e 6e 6f 74 20 63 72 65 61 74 65 20 77 72 69 74 61 62 6c 65 20 6d 65 6d 6f 72 79 20 76 69 Cannot.create.writable.memory.vi
63980 65 77 20 66 72 6f 6d 20 72 65 61 64 2d 6f 6e 6c 79 20 6d 65 6d 6f 72 79 76 69 65 77 00 00 00 00 ew.from.read-only.memoryview....
639a0 5f 5f 70 79 78 5f 75 6e 70 69 63 6b 6c 65 5f 45 6e 75 6d 00 6e 67 6f 6f 64 00 00 00 00 00 00 00 __pyx_unpickle_Enum.ngood.......
639c0 5b 2e 2e 2e 2c 3a 2d 31 5d 00 00 00 70 61 63 6b 00 00 00 00 69 6e 74 33 32 00 00 00 00 00 00 00 [...,:-1]...pack....int32.......
639e0 0a 20 20 20 20 20 20 20 20 70 6f 69 73 73 6f 6e 28 6c 61 6d 3d 31 2e 30 2c 20 73 69 7a 65 3d 4e .........poisson(lam=1.0,.size=N
63a00 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 one)..........Draw.samples.from.
63a20 61 20 50 6f 69 73 73 6f 6e 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 a.Poisson.distribution..........
63a40 20 54 68 65 20 50 6f 69 73 73 6f 6e 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 20 74 68 65 .The.Poisson.distribution.is.the
63a60 20 6c 69 6d 69 74 20 6f 66 20 74 68 65 20 62 69 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 .limit.of.the.binomial.distribut
63a80 69 6f 6e 0a 20 20 20 20 20 20 20 20 66 6f 72 20 6c 61 72 67 65 20 4e 2e 0a 0a 20 20 20 20 20 20 ion.........for.large.N.........
63aa0 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a ..Parameters.........----------.
63ac0 20 20 20 20 20 20 20 20 6c 61 6d 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b ........lam.:.float.or.array_lik
63ae0 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 45 78 70 65 63 74 65 64 e.of.floats.............Expected
63b00 20 6e 75 6d 62 65 72 20 6f 66 20 65 76 65 6e 74 73 20 6f 63 63 75 72 72 69 6e 67 20 69 6e 20 61 .number.of.events.occurring.in.a
63b20 20 66 69 78 65 64 2d 74 69 6d 65 20 69 6e 74 65 72 76 61 6c 2c 0a 20 20 20 20 20 20 20 20 20 20 .fixed-time.interval,...........
63b40 20 20 6d 75 73 74 20 62 65 20 3e 3d 20 30 2e 20 41 20 73 65 71 75 65 6e 63 65 20 6d 75 73 74 20 ..must.be.>=.0..A.sequence.must.
63b60 62 65 20 62 72 6f 61 64 63 61 73 74 61 62 6c 65 20 6f 76 65 72 20 74 68 65 20 72 65 71 75 65 73 be.broadcastable.over.the.reques
63b80 74 65 64 0a 20 20 20 20 20 20 20 20 20 20 20 20 73 69 7a 65 2e 0a 20 20 20 20 20 20 20 20 73 69 ted.............size..........si
63ba0 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f ze.:.int.or.tuple.of.ints,.optio
63bc0 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 nal.............Output.shape...I
63be0 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d f.the.given.shape.is,.e.g.,.``(m
63c00 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 ,.n,.k)``,.then.............``m.
63c20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 *.n.*.k``.samples.are.drawn...If
63c40 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 .size.is.``None``.(default),....
63c60 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 .........a.single.value.is.retur
63c80 6e 65 64 20 69 66 20 60 60 6c 61 6d 60 60 20 69 73 20 61 20 73 63 61 6c 61 72 2e 20 4f 74 68 65 ned.if.``lam``.is.a.scalar..Othe
63ca0 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6e 70 2e 61 72 72 61 79 28 6c 61 rwise,.............``np.array(la
63cc0 6d 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 m).size``.samples.are.drawn.....
63ce0 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 ......Returns.........-------...
63d00 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 ......out.:.ndarray.or.scalar...
63d20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 ..........Drawn.samples.from.the
63d40 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 50 6f 69 73 73 6f 6e 20 64 69 73 74 72 69 62 75 74 .parameterized.Poisson.distribut
63d60 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d ion...........Notes.........----
63d80 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 50 6f 69 73 73 6f 6e 20 64 69 73 74 72 69 62 75 74 69 -.........The.Poisson.distributi
63da0 6f 6e 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 66 28 6b 3b 20 5c 6c 61 6d 62 on.............math::.f(k;.\lamb
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65c60 64 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d d...........References.........-
65c80 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 50 61 70 6f 75 6c 69 ---------............[1].Papouli
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66540 65 65 6e 20 61 73 20 61 20 73 70 65 63 69 61 6c 20 63 61 73 65 20 6f 66 20 74 68 65 20 42 65 74 een.as.a.special.case.of.the.Bet
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66780 48 61 6e 64 62 6f 6f 6b 20 53 65 72 69 65 73 2c 20 4a 75 6e 65 20 32 30 30 33 2e 0a 20 20 20 20 Handbook.Series,.June.2003......
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66940 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a import.matplotlib.pyplot.as.plt.
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67420 28 6c 6f 63 3d 30 2e 30 2c 20 73 63 61 6c 65 3d 31 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a (loc=0.0,.scale=1.0,.size=None).
67440 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 4c .........Draw.samples.from.the.L
67460 61 70 6c 61 63 65 20 6f 72 20 64 6f 75 62 6c 65 20 65 78 70 6f 6e 65 6e 74 69 61 6c 20 64 69 73 aplace.or.double.exponential.dis
67480 74 72 69 62 75 74 69 6f 6e 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 73 70 65 63 69 66 69 65 64 tribution.with.........specified
674a0 20 6c 6f 63 61 74 69 6f 6e 20 28 6f 72 20 6d 65 61 6e 29 20 61 6e 64 20 73 63 61 6c 65 20 28 64 .location.(or.mean).and.scale.(d
674c0 65 63 61 79 29 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 4c 61 70 6c 61 63 65 20 64 69 73 74 ecay)...........The.Laplace.dist
674e0 72 69 62 75 74 69 6f 6e 20 69 73 20 73 69 6d 69 6c 61 72 20 74 6f 20 74 68 65 20 47 61 75 73 73 ribution.is.similar.to.the.Gauss
67500 69 61 6e 2f 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 0a 20 20 20 20 20 20 20 ian/normal.distribution,........
67520 20 62 75 74 20 69 73 20 73 68 61 72 70 65 72 20 61 74 20 74 68 65 20 70 65 61 6b 20 61 6e 64 20 .but.is.sharper.at.the.peak.and.
67540 68 61 73 20 66 61 74 74 65 72 20 74 61 69 6c 73 2e 20 49 74 20 72 65 70 72 65 73 65 6e 74 73 20 has.fatter.tails..It.represents.
67560 74 68 65 0a 20 20 20 20 20 20 20 20 64 69 66 66 65 72 65 6e 63 65 20 62 65 74 77 65 65 6e 20 74 the.........difference.between.t
67580 77 6f 20 69 6e 64 65 70 65 6e 64 65 6e 74 2c 20 69 64 65 6e 74 69 63 61 6c 6c 79 20 64 69 73 74 wo.independent,.identically.dist
675a0 72 69 62 75 74 65 64 20 65 78 70 6f 6e 65 6e 74 69 61 6c 0a 20 20 20 20 20 20 20 20 72 61 6e 64 ributed.exponential.........rand
675c0 6f 6d 20 76 61 72 69 61 62 6c 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 om.variables...........Parameter
675e0 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6c 6f 63 s.........----------.........loc
67600 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 .:.float.or.array_like.of.floats
67620 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 54 68 65 20 70 6f 73 69 74 ,.optional.............The.posit
67640 69 6f 6e 2c 20 3a 6d 61 74 68 3a 60 5c 6d 75 60 2c 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 ion,.:math:`\mu`,.of.the.distrib
67660 75 74 69 6f 6e 20 70 65 61 6b 2e 20 44 65 66 61 75 6c 74 20 69 73 20 30 2e 0a 20 20 20 20 20 20 ution.peak..Default.is.0........
67680 20 20 73 63 61 6c 65 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 ..scale.:.float.or.array_like.of
676a0 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 3a 6d .floats,.optional.............:m
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676e0 65 63 61 79 2e 20 44 65 66 61 75 6c 74 20 69 73 20 31 2e 20 4d 75 73 74 20 62 65 20 6e 6f 6e 2d ecay..Default.is.1..Must.be.non-
67700 0a 20 20 20 20 20 20 20 20 20 20 20 20 6e 65 67 61 74 69 76 65 2e 0a 20 20 20 20 20 20 20 20 73 .............negative..........s
67720 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 ize.:.int.or.tuple.of.ints,.opti
67740 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 onal.............Output.shape...
67760 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 If.the.given.shape.is,.e.g.,.``(
67780 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d m,.n,.k)``,.then.............``m
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677e0 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 ..........a.single.value.is.retu
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67820 65 20 62 6f 74 68 20 73 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 68 65 e.both.scalars..............Othe
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67880 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 .....Returns.........-------....
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678c0 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 .........Drawn.samples.from.the.
678e0 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 4c 61 70 6c 61 63 65 20 64 69 73 74 72 69 62 75 74 69 parameterized.Laplace.distributi
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67940 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 density.function.............mat
67960 68 3a 3a 20 66 28 78 3b 20 5c 6d 75 2c 20 5c 6c 61 6d 62 64 61 29 20 3d 20 5c 66 72 61 63 7b 31 h::.f(x;.\mu,.\lambda).=.\frac{1
67980 7d 7b 32 5c 6c 61 6d 62 64 61 7d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 }{2\lambda}.....................
679a0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5c 65 78 70 5c 6c 65 66 74 28 2d 5c 66 ...................\exp\left(-\f
679c0 72 61 63 7b 7c 78 20 2d 20 5c 6d 75 7c 7d 7b 5c 6c 61 6d 62 64 61 7d 5c 72 69 67 68 74 29 2e 0a rac{|x.-.\mu|}{\lambda}\right)..
679e0 0a 20 20 20 20 20 20 20 20 54 68 65 20 66 69 72 73 74 20 6c 61 77 20 6f 66 20 4c 61 70 6c 61 63 .........The.first.law.of.Laplac
67a00 65 2c 20 66 72 6f 6d 20 31 37 37 34 2c 20 73 74 61 74 65 73 20 74 68 61 74 20 74 68 65 20 66 72 e,.from.1774,.states.that.the.fr
67a20 65 71 75 65 6e 63 79 0a 20 20 20 20 20 20 20 20 6f 66 20 61 6e 20 65 72 72 6f 72 20 63 61 6e 20 equency.........of.an.error.can.
67a40 62 65 20 65 78 70 72 65 73 73 65 64 20 61 73 20 61 6e 20 65 78 70 6f 6e 65 6e 74 69 61 6c 20 66 be.expressed.as.an.exponential.f
67a60 75 6e 63 74 69 6f 6e 20 6f 66 20 74 68 65 0a 20 20 20 20 20 20 20 20 61 62 73 6f 6c 75 74 65 20 unction.of.the.........absolute.
67a80 6d 61 67 6e 69 74 75 64 65 20 6f 66 20 74 68 65 20 65 72 72 6f 72 2c 20 77 68 69 63 68 20 6c 65 magnitude.of.the.error,.which.le
67aa0 61 64 73 20 74 6f 20 74 68 65 20 4c 61 70 6c 61 63 65 0a 20 20 20 20 20 20 20 20 64 69 73 74 72 ads.to.the.Laplace.........distr
67ac0 69 62 75 74 69 6f 6e 2e 20 46 6f 72 20 6d 61 6e 79 20 70 72 6f 62 6c 65 6d 73 20 69 6e 20 65 63 ibution..For.many.problems.in.ec
67ae0 6f 6e 6f 6d 69 63 73 20 61 6e 64 20 68 65 61 6c 74 68 0a 20 20 20 20 20 20 20 20 73 63 69 65 6e onomics.and.health.........scien
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67b20 6d 6f 64 65 6c 20 74 68 65 20 64 61 74 61 20 62 65 74 74 65 72 0a 20 20 20 20 20 20 20 20 74 68 model.the.data.better.........th
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67b60 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 ution...........References......
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67ba0 61 6d 6f 77 69 74 7a 2c 20 4d 2e 20 61 6e 64 20 53 74 65 67 75 6e 2c 20 49 2e 20 41 2e 20 28 45 amowitz,.M..and.Stegun,.I..A..(E
67bc0 64 73 2e 29 2e 20 22 48 61 6e 64 62 6f 6f 6b 20 6f 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 ds.).."Handbook.of..............
67be0 20 20 4d 61 74 68 65 6d 61 74 69 63 61 6c 20 46 75 6e 63 74 69 6f 6e 73 20 77 69 74 68 20 46 6f ..Mathematical.Functions.with.Fo
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67c20 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 54 61 62 6c 65 73 2c 20 39 74 68 20 70 72 69 6e ................Tables,.9th.prin
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67cc0 20 22 20 42 69 72 6b 68 61 75 73 65 72 2c 20 32 30 30 31 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 .".Birkhauser,.2001.............
67ce0 5b 33 5d 20 57 65 69 73 73 74 65 69 6e 2c 20 45 72 69 63 20 57 2e 20 22 4c 61 70 6c 61 63 65 20 [3].Weisstein,.Eric.W.."Laplace.
67d00 44 69 73 74 72 69 62 75 74 69 6f 6e 2e 22 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 46 72 Distribution."................Fr
67d20 6f 6d 20 4d 61 74 68 57 6f 72 6c 64 2d 2d 41 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 65 73 6f om.MathWorld--A.Wolfram.Web.Reso
67d40 75 72 63 65 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d 61 74 68 urce.................http://math
67d60 77 6f 72 6c 64 2e 77 6f 6c 66 72 61 6d 2e 63 6f 6d 2f 4c 61 70 6c 61 63 65 44 69 73 74 72 69 62 world.wolfram.com/LaplaceDistrib
67d80 75 74 69 6f 6e 2e 68 74 6d 6c 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 34 5d 20 57 69 6b 69 70 65 ution.html............[4].Wikipe
67da0 64 69 61 2c 20 22 4c 61 70 6c 61 63 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 22 2c 0a 20 20 20 dia,."Laplace.distribution",....
67dc0 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 ............https://en.wikipedia
67de0 2e 6f 72 67 2f 77 69 6b 69 2f 4c 61 70 6c 61 63 65 5f 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a .org/wiki/Laplace_distribution..
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67f80 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 78 20 3d 20 6e 70 2e 61 72 61 6e 67 65 28 2d 38 2e 2c ).........>>>.x.=.np.arange(-8.,
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67fc0 78 70 28 2d 61 62 73 28 78 2d 6c 6f 63 29 2f 73 63 61 6c 65 29 2f 28 32 2e 2a 73 63 61 6c 65 29 xp(-abs(x-loc)/scale)/(2.*scale)
67fe0 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 70 6c 6f 74 28 78 2c 20 70 64 66 29 0a 0a 20 .........>>>.plt.plot(x,.pdf)...
68000 20 20 20 20 20 20 20 50 6c 6f 74 20 47 61 75 73 73 69 61 6e 20 66 6f 72 20 63 6f 6d 70 61 72 69 .......Plot.Gaussian.for.compari
68020 73 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 67 20 3d 20 28 31 2f 28 73 63 61 6c 65 20 son:..........>>>.g.=.(1/(scale.
68040 2a 20 6e 70 2e 73 71 72 74 28 32 20 2a 20 6e 70 2e 70 69 29 29 20 2a 0a 20 20 20 20 20 20 20 20 *.np.sqrt(2.*.np.pi)).*.........
68060 2e 2e 2e 20 20 20 20 20 20 6e 70 2e 65 78 70 28 2d 28 78 20 2d 20 6c 6f 63 29 2a 2a 32 20 2f 20 .........np.exp(-(x.-.loc)**2./.
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680a0 2e 70 6c 6f 74 28 78 2c 67 29 0a 0a 20 20 20 20 20 20 20 20 00 00 00 00 5f 5f 70 79 78 5f 63 68 .plot(x,g)..............__pyx_ch
680c0 65 63 6b 73 75 6d 00 00 63 6f 75 6e 74 5f 6e 6f 6e 7a 65 72 6f 00 00 00 47 65 6e 65 72 61 74 6f ecksum..count_nonzero...Generato
680e0 72 2e 72 61 79 6c 65 69 67 68 20 28 6c 69 6e 65 20 32 35 37 30 29 00 00 62 6f 6f 6c 5f 00 00 00 r.rayleigh.(line.2570)..bool_...
68100 65 6e 64 70 6f 69 6e 74 00 00 00 00 00 00 00 00 57 68 65 6e 20 6d 65 74 68 6f 64 20 69 73 20 22 endpoint........When.method.is."
68120 6d 61 72 67 69 6e 61 6c 73 22 2c 20 73 75 6d 28 63 6f 6c 6f 72 73 29 20 6d 75 73 74 20 62 65 20 marginals",.sum(colors).must.be.
68140 6c 65 73 73 20 74 68 61 6e 20 31 30 30 30 30 30 30 30 30 30 2e 00 00 00 73 74 61 63 6b 6c 65 76 less.than.1000000000....stacklev
68160 65 6c 00 00 69 6e 74 38 00 00 00 00 00 00 00 00 43 6f 6e 73 74 72 75 63 74 20 61 20 6e 65 77 20 el..int8........Construct.a.new.
68180 47 65 6e 65 72 61 74 6f 72 20 77 69 74 68 20 74 68 65 20 64 65 66 61 75 6c 74 20 42 69 74 47 65 Generator.with.the.default.BitGe
681a0 6e 65 72 61 74 6f 72 20 28 50 43 47 36 34 29 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 nerator.(PCG64).......Parameters
681c0 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 73 65 65 64 20 3a 20 7b 4e 6f 6e 65 .....----------.....seed.:.{None
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68220 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 41 20 73 65 65 64 20 74 6f 20 69 6e 69 74 .optional.........A.seed.to.init
68240 69 61 6c 69 7a 65 20 74 68 65 20 60 42 69 74 47 65 6e 65 72 61 74 6f 72 60 2e 20 49 66 20 4e 6f ialize.the.`BitGenerator`..If.No
68260 6e 65 2c 20 74 68 65 6e 20 66 72 65 73 68 2c 0a 20 20 20 20 20 20 20 20 75 6e 70 72 65 64 69 63 ne,.then.fresh,.........unpredic
68280 74 61 62 6c 65 20 65 6e 74 72 6f 70 79 20 77 69 6c 6c 20 62 65 20 70 75 6c 6c 65 64 20 66 72 6f table.entropy.will.be.pulled.fro
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682c0 20 20 20 60 60 61 72 72 61 79 5f 6c 69 6b 65 5b 69 6e 74 73 5d 60 60 20 69 73 20 70 61 73 73 65 ...``array_like[ints]``.is.passe
682e0 64 2c 20 74 68 65 6e 20 69 74 20 77 69 6c 6c 20 62 65 20 70 61 73 73 65 64 20 74 6f 0a 20 20 20 d,.then.it.will.be.passed.to....
68300 20 20 20 20 20 60 53 65 65 64 53 65 71 75 65 6e 63 65 60 20 74 6f 20 64 65 72 69 76 65 20 74 68 .....`SeedSequence`.to.derive.th
68320 65 20 69 6e 69 74 69 61 6c 20 60 42 69 74 47 65 6e 65 72 61 74 6f 72 60 20 73 74 61 74 65 2e 20 e.initial.`BitGenerator`.state..
68340 4f 6e 65 20 6d 61 79 20 61 6c 73 6f 0a 20 20 20 20 20 20 20 20 70 61 73 73 20 69 6e 20 61 20 60 One.may.also.........pass.in.a.`
68360 53 65 65 64 53 65 71 75 65 6e 63 65 60 20 69 6e 73 74 61 6e 63 65 2e 0a 20 20 20 20 20 20 20 20 SeedSequence`.instance..........
68380 41 64 64 69 74 69 6f 6e 61 6c 6c 79 2c 20 77 68 65 6e 20 70 61 73 73 65 64 20 61 20 60 42 69 74 Additionally,.when.passed.a.`Bit
683a0 47 65 6e 65 72 61 74 6f 72 60 2c 20 69 74 20 77 69 6c 6c 20 62 65 20 77 72 61 70 70 65 64 20 62 Generator`,.it.will.be.wrapped.b
683c0 79 0a 20 20 20 20 20 20 20 20 60 47 65 6e 65 72 61 74 6f 72 60 2e 20 49 66 20 70 61 73 73 65 64 y.........`Generator`..If.passed
683e0 20 61 20 60 47 65 6e 65 72 61 74 6f 72 60 2c 20 69 74 20 77 69 6c 6c 20 62 65 20 72 65 74 75 72 .a.`Generator`,.it.will.be.retur
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68420 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 65 6e 65 72 61 74 6f 72 0a 20 20 20 20 20 20 20 20 54 68 -------.....Generator.........Th
68440 65 20 69 6e 69 74 69 61 6c 69 7a 65 64 20 67 65 6e 65 72 61 74 6f 72 20 6f 62 6a 65 63 74 2e 0a e.initialized.generator.object..
68460 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 49 66 20 60 60 73 65 .....Notes.....-----.....If.``se
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684a0 61 20 60 47 65 6e 65 72 61 74 6f 72 60 2c 20 61 20 6e 65 77 20 60 42 69 74 47 65 6e 65 72 61 74 a.`Generator`,.a.new.`BitGenerat
684c0 6f 72 60 0a 20 20 20 20 69 73 20 69 6e 73 74 61 6e 74 69 61 74 65 64 2e 20 54 68 69 73 20 66 75 or`.....is.instantiated..This.fu
684e0 6e 63 74 69 6f 6e 20 64 6f 65 73 20 6e 6f 74 20 6d 61 6e 61 67 65 20 61 20 64 65 66 61 75 6c 74 nction.does.not.manage.a.default
68500 20 67 6c 6f 62 61 6c 20 69 6e 73 74 61 6e 63 65 2e 0a 20 20 20 20 0a 20 20 20 20 45 78 61 6d 70 .global.instance...........Examp
68520 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 60 60 64 65 66 61 75 6c 74 5f 72 les.....--------.....``default_r
68540 6e 67 60 60 20 69 73 20 74 68 65 20 72 65 63 6f 6d 6d 65 6e 64 65 64 20 63 6f 6e 73 74 72 75 63 ng``.is.the.recommended.construc
68560 74 6f 72 20 66 6f 72 20 74 68 65 20 72 61 6e 64 6f 6d 20 6e 75 6d 62 65 72 20 63 6c 61 73 73 0a tor.for.the.random.number.class.
68580 20 20 20 20 60 60 47 65 6e 65 72 61 74 6f 72 60 60 2e 20 48 65 72 65 20 61 72 65 20 73 65 76 65 ....``Generator``..Here.are.seve
685a0 72 61 6c 20 77 61 79 73 20 77 65 20 63 61 6e 20 63 6f 6e 73 74 72 75 63 74 20 61 20 72 61 6e 64 ral.ways.we.can.construct.a.rand
685c0 6f 6d 20 0a 20 20 20 20 6e 75 6d 62 65 72 20 67 65 6e 65 72 61 74 6f 72 20 75 73 69 6e 67 20 60 om......number.generator.using.`
685e0 60 64 65 66 61 75 6c 74 5f 72 6e 67 60 60 20 61 6e 64 20 74 68 65 20 60 60 47 65 6e 65 72 61 74 `default_rng``.and.the.``Generat
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69f00 47 65 6e 65 72 61 74 6f 72 00 00 00 00 00 00 00 69 74 65 6d 73 69 7a 65 00 00 00 00 00 00 00 00 Generator.......itemsize........
69f20 6e 73 61 6d 70 6c 65 20 6d 75 73 74 20 62 65 20 6e 6f 6e 6e 65 67 61 74 69 76 65 2e 00 00 00 00 nsample.must.be.nonnegative.....
69f40 63 6f 70 79 00 00 00 00 5f 5f 67 65 74 73 74 61 74 65 5f 5f 00 00 00 00 66 6c 61 67 73 00 00 00 copy....__getstate__....flags...
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69fe0 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 72 64 5f 67 61 6d 6d 61 20 28 6c 69 6e 65 20 31 Generator.standard_gamma.(line.1
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6a020 65 73 28 70 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 es(p,.size=None)..........Draw.s
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6a060 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 61 6d 70 6c 65 73 20 .distribution...........Samples.
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6a0e0 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d .........Parameters.........----
6a100 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 70 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 ------.........p.:.float.or.arra
6a120 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 53 68 61 y_like.of.floats.............Sha
6a140 70 65 20 70 61 72 61 6d 65 74 65 72 20 66 6f 72 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f pe.parameter.for.the.distributio
6a160 6e 2e 20 20 4d 75 73 74 20 62 65 20 69 6e 20 74 68 65 20 72 61 6e 67 65 20 28 30 2c 20 31 29 2e n...Must.be.in.the.range.(0,.1).
6a180 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 .........size.:.int.or.tuple.of.
6a1a0 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 ints,.optional.............Outpu
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6a1e0 20 65 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 .e.g.,.``(m,.n,.k)``,.then......
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6a280 6c 61 72 2e 20 20 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6e lar...Otherwise,.............``n
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6a300 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 calar.............Drawn.samples.
6a320 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 6c 6f 67 61 72 69 74 68 6d from.the.parameterized.logarithm
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6a3e0 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 65 74 63 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 sity.function,.etc...........Not
6a400 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f es.........-----.........The.pro
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6a440 6f 67 20 53 65 72 69 65 73 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 og.Series.distribution.is.......
6a460 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 50 28 6b 29 20 3d 20 5c 66 72 61 63 7b 2d 70 5e 6b 7d 7b ......math::.P(k).=.\frac{-p^k}{
6a480 6b 20 5c 6c 6e 28 31 2d 70 29 7d 2c 0a 0a 20 20 20 20 20 20 20 20 77 68 65 72 65 20 70 20 3d 20 k.\ln(1-p)},..........where.p.=.
6a4a0 70 72 6f 62 61 62 69 6c 69 74 79 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 6c 6f 67 20 73 65 probability...........The.log.se
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6a500 20 20 72 69 63 68 6e 65 73 73 20 61 6e 64 20 6f 63 63 75 72 72 65 6e 63 65 2c 20 66 69 72 73 74 ..richness.and.occurrence,.first
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6a540 0a 20 20 20 20 20 20 20 20 57 69 6c 6c 69 61 6d 73 20 69 6e 20 31 39 34 33 20 5b 32 5d 2e 20 20 .........Williams.in.1943.[2]...
6a560 49 74 20 6d 61 79 20 61 6c 73 6f 20 62 65 20 75 73 65 64 20 74 6f 20 6d 6f 64 65 6c 20 74 68 65 It.may.also.be.used.to.model.the
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6a5e0 2e 20 5b 31 5d 20 42 75 7a 61 73 2c 20 4d 61 72 74 69 6e 20 41 2e 3b 20 43 75 6c 76 65 72 2c 20 ..[1].Buzas,.Martin.A.;.Culver,.
6a600 53 74 65 70 68 65 6e 20 4a 2e 2c 20 20 55 6e 64 65 72 73 74 61 6e 64 69 6e 67 20 72 65 67 69 6f Stephen.J.,..Understanding.regio
6a620 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 73 70 65 63 69 65 73 20 64 69 76 65 72 nal................species.diver
6a640 73 69 74 79 20 74 68 72 6f 75 67 68 20 74 68 65 20 6c 6f 67 20 73 65 72 69 65 73 20 64 69 73 74 sity.through.the.log.series.dist
6a660 72 69 62 75 74 69 6f 6e 20 6f 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 6f 63 63 75 72 ribution.of................occur
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6a6c0 20 20 20 20 20 20 20 20 56 6f 6c 75 6d 65 20 35 2c 20 4e 75 6d 62 65 72 20 35 2c 20 53 65 70 74 ........Volume.5,.Number.5,.Sept
6a6e0 65 6d 62 65 72 20 31 39 39 39 20 2c 20 70 70 2e 20 31 38 37 2d 31 39 35 28 39 29 2e 0a 20 20 20 ember.1999.,.pp..187-195(9).....
6a700 20 20 20 20 20 2e 2e 20 5b 32 5d 20 46 69 73 68 65 72 2c 20 52 2e 41 2c 2c 20 41 2e 53 2e 20 43 ........[2].Fisher,.R.A,,.A.S..C
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6a740 54 68 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 72 65 6c 61 74 69 6f 6e 20 62 65 74 77 The................relation.betw
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6a7c0 61 6e 69 6d 61 6c 20 70 6f 70 75 6c 61 74 69 6f 6e 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 animal.population...............
6a7e0 20 20 4a 6f 75 72 6e 61 6c 20 6f 66 20 41 6e 69 6d 61 6c 20 45 63 6f 6c 6f 67 79 2c 20 31 32 3a ..Journal.of.Animal.Ecology,.12:
6a800 34 32 2d 35 38 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 33 5d 20 44 2e 20 4a 2e 20 48 61 6e 64 42-58.............[3].D..J..Hand
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6a840 2c 20 41 20 48 61 6e 64 62 6f 6f 6b 20 6f 66 20 53 6d 61 6c 6c 0a 20 20 20 20 20 20 20 20 20 20 ,.A.Handbook.of.Small...........
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6a880 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 34 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 4c 6f 67 61 ............[4].Wikipedia,."Loga
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6a920 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 64 69 ........Draw.samples.from.the.di
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6a9e0 20 69 67 6e 6f 72 65 64 20 3d 20 70 6c 74 2e 68 69 73 74 28 73 29 0a 0a 20 20 20 20 20 20 20 20 .ignored.=.plt.hist(s)..........
6aa00 23 20 20 20 70 6c 6f 74 20 61 67 61 69 6e 73 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a 20 #...plot.against.distribution...
6aa20 20 20 20 20 20 20 20 3e 3e 3e 20 64 65 66 20 6c 6f 67 73 65 72 69 65 73 28 6b 2c 20 70 29 3a 0a .......>>>.def.logseries(k,.p):.
6aa40 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 72 65 74 75 72 6e 20 2d 70 2a 2a 6b 2f 28 6b 2a ................return.-p**k/(k*
6aa60 6e 70 2e 6c 6f 67 28 31 2d 70 29 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 70 6c 6f np.log(1-p)).........>>>.plt.plo
6aa80 74 28 62 69 6e 73 2c 20 6c 6f 67 73 65 72 69 65 73 28 62 69 6e 73 2c 20 61 29 20 2a 20 63 6f 75 t(bins,.logseries(bins,.a).*.cou
6aaa0 6e 74 2e 6d 61 78 28 29 2f 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 20 20 20 20 20 6c nt.max()/......................l
6aac0 6f 67 73 65 72 69 65 73 28 62 69 6e 73 2c 20 61 29 2e 6d 61 78 28 29 2c 20 27 72 27 29 0a 20 20 ogseries(bins,.a).max(),.'r')...
6aae0 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 20 20 20 00 00 ......>>>.plt.show()............
6ab00 5f 5f 70 79 78 5f 67 65 74 62 75 66 66 65 72 00 50 69 63 6b 6c 65 45 72 72 6f 72 00 00 00 00 00 __pyx_getbuffer.PickleError.....
6ab20 47 65 6e 65 72 61 74 6f 72 2e 75 6e 69 66 6f 72 6d 20 28 6c 69 6e 65 20 38 36 31 29 00 00 00 00 Generator.uniform.(line.861)....
6ab40 6d 65 6d 6f 72 79 20 61 6c 6c 6f 63 61 74 69 6f 6e 20 66 61 69 6c 65 64 20 69 6e 20 70 65 72 6d memory.allocation.failed.in.perm
6ab60 75 74 65 64 00 00 00 00 61 73 63 6f 6e 74 69 67 75 6f 75 73 61 72 72 61 79 00 00 00 00 00 00 00 uted....ascontiguousarray.......
6ab80 5f 5f 67 65 6e 65 72 61 74 6f 72 5f 63 74 6f 72 00 00 00 00 00 00 00 00 64 65 66 61 75 6c 74 5f __generator_ctor........default_
6aba0 72 6e 67 00 65 6d 70 74 79 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 75 6e 69 66 6f 72 6d rng.empty................uniform
6abc0 28 6c 6f 77 3d 30 2e 30 2c 20 68 69 67 68 3d 31 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a (low=0.0,.high=1.0,.size=None)..
6abe0 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 75 6e 69 66 ........Draw.samples.from.a.unif
6ac00 6f 72 6d 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 61 6d 70 6c orm.distribution...........Sampl
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6ac40 72 20 74 68 65 20 68 61 6c 66 2d 6f 70 65 6e 20 69 6e 74 65 72 76 61 6c 0a 20 20 20 20 20 20 20 r.the.half-open.interval........
6ac60 20 60 60 5b 6c 6f 77 2c 20 68 69 67 68 29 60 60 20 28 69 6e 63 6c 75 64 65 73 20 6c 6f 77 2c 20 .``[low,.high)``.(includes.low,.
6ac80 62 75 74 20 65 78 63 6c 75 64 65 73 20 68 69 67 68 29 2e 20 20 49 6e 20 6f 74 68 65 72 20 77 6f but.excludes.high)...In.other.wo
6aca0 72 64 73 2c 0a 20 20 20 20 20 20 20 20 61 6e 79 20 76 61 6c 75 65 20 77 69 74 68 69 6e 20 74 68 rds,.........any.value.within.th
6acc0 65 20 67 69 76 65 6e 20 69 6e 74 65 72 76 61 6c 20 69 73 20 65 71 75 61 6c 6c 79 20 6c 69 6b 65 e.given.interval.is.equally.like
6ace0 6c 79 20 74 6f 20 62 65 20 64 72 61 77 6e 0a 20 20 20 20 20 20 20 20 62 79 20 60 75 6e 69 66 6f ly.to.be.drawn.........by.`unifo
6ad00 72 6d 60 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 rm`...........Parameters........
6ad20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6c 6f 77 20 3a 20 66 6c 6f 61 74 20 .----------.........low.:.float.
6ad40 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 or.array_like.of.floats,.optiona
6ad60 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4c 6f 77 65 72 20 62 6f 75 6e 64 61 72 79 20 6f 66 20 l.............Lower.boundary.of.
6ad80 74 68 65 20 6f 75 74 70 75 74 20 69 6e 74 65 72 76 61 6c 2e 20 20 41 6c 6c 20 76 61 6c 75 65 73 the.output.interval...All.values
6ada0 20 67 65 6e 65 72 61 74 65 64 20 77 69 6c 6c 20 62 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 67 .generated.will.be.............g
6adc0 72 65 61 74 65 72 20 74 68 61 6e 20 6f 72 20 65 71 75 61 6c 20 74 6f 20 6c 6f 77 2e 20 20 54 68 reater.than.or.equal.to.low...Th
6ade0 65 20 64 65 66 61 75 6c 74 20 76 61 6c 75 65 20 69 73 20 30 2e 0a 20 20 20 20 20 20 20 20 68 69 e.default.value.is.0..........hi
6ae00 67 68 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 gh.:.float.or.array_like.of.floa
6ae20 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 55 70 70 65 72 20 62 6f 75 6e 64 61 72 79 20 6f 66 ts.............Upper.boundary.of
6ae40 20 74 68 65 20 6f 75 74 70 75 74 20 69 6e 74 65 72 76 61 6c 2e 20 20 41 6c 6c 20 76 61 6c 75 65 .the.output.interval...All.value
6ae60 73 20 67 65 6e 65 72 61 74 65 64 20 77 69 6c 6c 20 62 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 s.generated.will.be.............
6ae80 6c 65 73 73 20 74 68 61 6e 20 68 69 67 68 2e 20 20 54 68 65 20 68 69 67 68 20 6c 69 6d 69 74 20 less.than.high...The.high.limit.
6aea0 6d 61 79 20 62 65 20 69 6e 63 6c 75 64 65 64 20 69 6e 20 74 68 65 20 72 65 74 75 72 6e 65 64 20 may.be.included.in.the.returned.
6aec0 61 72 72 61 79 20 6f 66 20 0a 20 20 20 20 20 20 20 20 20 20 20 20 66 6c 6f 61 74 73 20 64 75 65 array.of..............floats.due
6aee0 20 74 6f 20 66 6c 6f 61 74 69 6e 67 2d 70 6f 69 6e 74 20 72 6f 75 6e 64 69 6e 67 20 69 6e 20 74 .to.floating-point.rounding.in.t
6af00 68 65 20 65 71 75 61 74 69 6f 6e 20 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6c 6f 77 20 2b he.equation..............``low.+
6af20 20 28 68 69 67 68 2d 6c 6f 77 29 20 2a 20 72 61 6e 64 6f 6d 5f 73 61 6d 70 6c 65 28 29 60 60 2e .(high-low).*.random_sample()``.
6af40 20 20 68 69 67 68 20 2d 20 6c 6f 77 20 6d 75 73 74 20 62 65 20 0a 20 20 20 20 20 20 20 20 20 20 ..high.-.low.must.be............
6af60 20 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 2e 20 20 54 68 65 20 64 65 66 61 75 6c 74 20 76 61 6c ..non-negative...The.default.val
6af80 75 65 20 69 73 20 31 2e 30 2e 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 ue.is.1.0..........size.:.int.or
6afa0 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 .tuple.of.ints,.optional........
6afc0 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e .....Output.shape...If.the.given
6afe0 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 .shape.is,.e.g.,.``(m,.n,.k)``,.
6b000 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 then.............``m.*.n.*.k``.s
6b020 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 amples.are.drawn...If.size.is.``
6b040 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 None``.(default),.............a.
6b060 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 6c 6f single.value.is.returned.if.``lo
6b080 77 60 60 20 61 6e 64 20 60 60 68 69 67 68 60 60 20 61 72 65 20 62 6f 74 68 20 73 63 61 6c 61 72 w``.and.``high``.are.both.scalar
6b0a0 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 68 65 72 77 69 73 65 2c 20 60 60 6e 70 2e 62 s..............Otherwise,.``np.b
6b0c0 72 6f 61 64 63 61 73 74 28 6c 6f 77 2c 20 68 69 67 68 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c roadcast(low,.high).size``.sampl
6b0e0 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 es.are.drawn...........Returns..
6b100 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 .......-------.........out.:.nda
6b120 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e rray.or.scalar.............Drawn
6b140 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 .samples.from.the.parameterized.
6b160 75 6e 69 66 6f 72 6d 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 uniform.distribution...........S
6b180 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 ee.Also.........--------........
6b1a0 20 69 6e 74 65 67 65 72 73 20 3a 20 44 69 73 63 72 65 74 65 20 75 6e 69 66 6f 72 6d 20 64 69 73 .integers.:.Discrete.uniform.dis
6b1c0 74 72 69 62 75 74 69 6f 6e 2c 20 79 69 65 6c 64 69 6e 67 20 69 6e 74 65 67 65 72 73 2e 0a 20 20 tribution,.yielding.integers....
6b1e0 20 20 20 20 20 20 72 61 6e 64 6f 6d 20 3a 20 46 6c 6f 61 74 73 20 75 6e 69 66 6f 72 6d 6c 79 20 ......random.:.Floats.uniformly.
6b200 64 69 73 74 72 69 62 75 74 65 64 20 6f 76 65 72 20 60 60 5b 30 2c 20 31 29 60 60 2e 0a 0a 20 20 distributed.over.``[0,.1)``.....
6b220 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 ......Notes.........-----.......
6b240 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 ..The.probability.density.functi
6b260 6f 6e 20 6f 66 20 74 68 65 20 75 6e 69 66 6f 72 6d 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 on.of.the.uniform.distribution.i
6b280 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 5c 66 72 61 s.............math::.p(x).=.\fra
6b2a0 63 7b 31 7d 7b 62 20 2d 20 61 7d 0a 0a 20 20 20 20 20 20 20 20 61 6e 79 77 68 65 72 65 20 77 69 c{1}{b.-.a}..........anywhere.wi
6b2c0 74 68 69 6e 20 74 68 65 20 69 6e 74 65 72 76 61 6c 20 60 60 5b 61 2c 20 62 29 60 60 2c 20 61 6e thin.the.interval.``[a,.b)``,.an
6b2e0 64 20 7a 65 72 6f 20 65 6c 73 65 77 68 65 72 65 2e 0a 0a 20 20 20 20 20 20 20 20 57 68 65 6e 20 d.zero.elsewhere...........When.
6b300 60 60 68 69 67 68 60 60 20 3d 3d 20 60 60 6c 6f 77 60 60 2c 20 76 61 6c 75 65 73 20 6f 66 20 60 ``high``.==.``low``,.values.of.`
6b320 60 6c 6f 77 60 60 20 77 69 6c 6c 20 62 65 20 72 65 74 75 72 6e 65 64 2e 0a 0a 20 20 20 20 20 20 `low``.will.be.returned.........
6b340 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 ..Examples.........--------.....
6b360 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 64 69 73 74 72 69 ....Draw.samples.from.the.distri
6b380 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 6e 70 2e 72 61 6e 64 bution:..........>>>.s.=.np.rand
6b3a0 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 2e 75 6e 69 66 6f 72 6d 28 2d 31 2c 30 2c 31 30 om.default_rng().uniform(-1,0,10
6b3c0 30 30 29 0a 0a 20 20 20 20 20 20 20 20 41 6c 6c 20 76 61 6c 75 65 73 20 61 72 65 20 77 69 74 68 00)..........All.values.are.with
6b3e0 69 6e 20 74 68 65 20 67 69 76 65 6e 20 69 6e 74 65 72 76 61 6c 3a 0a 0a 20 20 20 20 20 20 20 20 in.the.given.interval:..........
6b400 3e 3e 3e 20 6e 70 2e 61 6c 6c 28 73 20 3e 3d 20 2d 31 29 0a 20 20 20 20 20 20 20 20 54 72 75 65 >>>.np.all(s.>=.-1).........True
6b420 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6e 70 2e 61 6c 6c 28 73 20 3c 20 30 29 0a 20 20 20 20 20 .........>>>.np.all(s.<.0)......
6b440 20 20 20 54 72 75 65 0a 0a 20 20 20 20 20 20 20 20 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 ...True..........Display.the.his
6b460 74 6f 67 72 61 6d 20 6f 66 20 74 68 65 20 73 61 6d 70 6c 65 73 2c 20 61 6c 6f 6e 67 20 77 69 74 togram.of.the.samples,.along.wit
6b480 68 20 74 68 65 0a 20 20 20 20 20 20 20 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 h.the.........probability.densit
6b4a0 79 20 66 75 6e 63 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 y.function:..........>>>.import.
6b4c0 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 matplotlib.pyplot.as.plt........
6b4e0 20 3e 3e 3e 20 63 6f 75 6e 74 2c 20 62 69 6e 73 2c 20 69 67 6e 6f 72 65 64 20 3d 20 70 6c 74 2e .>>>.count,.bins,.ignored.=.plt.
6b500 68 69 73 74 28 73 2c 20 31 35 2c 20 64 65 6e 73 69 74 79 3d 54 72 75 65 29 0a 20 20 20 20 20 20 hist(s,.15,.density=True).......
6b520 20 20 3e 3e 3e 20 70 6c 74 2e 70 6c 6f 74 28 62 69 6e 73 2c 20 6e 70 2e 6f 6e 65 73 5f 6c 69 6b ..>>>.plt.plot(bins,.np.ones_lik
6b540 65 28 62 69 6e 73 29 2c 20 6c 69 6e 65 77 69 64 74 68 3d 32 2c 20 63 6f 6c 6f 72 3d 27 72 27 29 e(bins),.linewidth=2,.color='r')
6b560 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 20 20 .........>>>.plt.show().........
6b580 20 00 00 00 00 00 00 00 47 65 6e 65 72 61 74 6f 72 2e 70 6f 69 73 73 6f 6e 20 28 6c 69 6e 65 20 ........Generator.poisson.(line.
6b5a0 33 30 32 37 29 00 00 00 63 68 65 63 6b 5f 76 61 6c 69 64 20 6d 75 73 74 20 65 71 75 61 6c 20 27 3027)...check_valid.must.equal.'
6b5c0 77 61 72 6e 27 2c 20 27 72 61 69 73 65 27 2c 20 6f 72 20 27 69 67 6e 6f 72 65 27 00 00 00 00 00 warn',.'raise',.or.'ignore'.....
6b5e0 0a 20 20 20 20 20 20 20 20 64 69 72 69 63 68 6c 65 74 28 61 6c 70 68 61 2c 20 73 69 7a 65 3d 4e .........dirichlet(alpha,.size=N
6b600 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 one)..........Draw.samples.from.
6b620 74 68 65 20 44 69 72 69 63 68 6c 65 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 the.Dirichlet.distribution......
6b640 20 20 20 20 20 44 72 61 77 20 60 73 69 7a 65 60 20 73 61 6d 70 6c 65 73 20 6f 66 20 64 69 6d 65 .....Draw.`size`.samples.of.dime
6b660 6e 73 69 6f 6e 20 6b 20 66 72 6f 6d 20 61 20 44 69 72 69 63 68 6c 65 74 20 64 69 73 74 72 69 62 nsion.k.from.a.Dirichlet.distrib
6b680 75 74 69 6f 6e 2e 20 41 0a 20 20 20 20 20 20 20 20 44 69 72 69 63 68 6c 65 74 2d 64 69 73 74 72 ution..A.........Dirichlet-distr
6b6a0 69 62 75 74 65 64 20 72 61 6e 64 6f 6d 20 76 61 72 69 61 62 6c 65 20 63 61 6e 20 62 65 20 73 65 ibuted.random.variable.can.be.se
6b6c0 65 6e 20 61 73 20 61 20 6d 75 6c 74 69 76 61 72 69 61 74 65 0a 20 20 20 20 20 20 20 20 67 65 6e en.as.a.multivariate.........gen
6b6e0 65 72 61 6c 69 7a 61 74 69 6f 6e 20 6f 66 20 61 20 42 65 74 61 20 64 69 73 74 72 69 62 75 74 69 eralization.of.a.Beta.distributi
6b700 6f 6e 2e 20 54 68 65 20 44 69 72 69 63 68 6c 65 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 20 on..The.Dirichlet.distribution..
6b720 20 20 20 20 20 20 20 69 73 20 61 20 63 6f 6e 6a 75 67 61 74 65 20 70 72 69 6f 72 20 6f 66 20 61 .......is.a.conjugate.prior.of.a
6b740 20 6d 75 6c 74 69 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 6e 20 42 61 79 .multinomial.distribution.in.Bay
6b760 65 73 69 61 6e 0a 20 20 20 20 20 20 20 20 69 6e 66 65 72 65 6e 63 65 2e 0a 0a 20 20 20 20 20 20 esian.........inference.........
6b780 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a ..Parameters.........----------.
6b7a0 20 20 20 20 20 20 20 20 61 6c 70 68 61 20 3a 20 73 65 71 75 65 6e 63 65 20 6f 66 20 66 6c 6f 61 ........alpha.:.sequence.of.floa
6b7c0 74 73 2c 20 6c 65 6e 67 74 68 20 6b 0a 20 20 20 20 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 ts,.length.k.............Paramet
6b7e0 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 28 6c 65 6e 67 74 68 20 60 er.of.the.distribution.(length.`
6b800 60 6b 60 60 20 66 6f 72 20 73 61 6d 70 6c 65 20 6f 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 6c `k``.for.sample.of.............l
6b820 65 6e 67 74 68 20 60 60 6b 60 60 29 2e 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 ength.``k``)..........size.:.int
6b840 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 .or.tuple.of.ints,.optional.....
6b860 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 ........Output.shape...If.the.gi
6b880 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 29 60 60 2c 20 ven.shape.is,.e.g.,.``(m,.n)``,.
6b8a0 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 then.............``m.*.n.*.k``.s
6b8c0 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 44 65 66 61 75 6c 74 20 69 73 20 4e 6f amples.are.drawn...Default.is.No
6b8e0 6e 65 2c 20 69 6e 20 77 68 69 63 68 20 63 61 73 65 20 61 0a 20 20 20 20 20 20 20 20 20 20 20 20 ne,.in.which.case.a.............
6b900 76 65 63 74 6f 72 20 6f 66 20 6c 65 6e 67 74 68 20 60 60 6b 60 60 20 69 73 20 72 65 74 75 72 6e vector.of.length.``k``.is.return
6b920 65 64 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d ed...........Returns.........---
6b940 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 61 6d 70 6c 65 73 20 3a 20 6e 64 61 72 72 61 79 2c 0a ----.........samples.:.ndarray,.
6b960 20 20 20 20 20 20 20 20 20 20 20 20 54 68 65 20 64 72 61 77 6e 20 73 61 6d 70 6c 65 73 2c 20 6f ............The.drawn.samples,.o
6b980 66 20 73 68 61 70 65 20 60 60 28 73 69 7a 65 2c 20 6b 29 60 60 2e 0a 0a 20 20 20 20 20 20 20 20 f.shape.``(size,.k)``...........
6b9a0 52 61 69 73 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 56 61 Raises.........------.........Va
6b9c0 6c 75 65 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 61 6e 79 20 76 61 6c 75 lueError.............If.any.valu
6b9e0 65 20 69 6e 20 60 60 61 6c 70 68 61 60 60 20 69 73 20 6c 65 73 73 20 74 68 61 6e 20 6f 72 20 65 e.in.``alpha``.is.less.than.or.e
6ba00 71 75 61 6c 20 74 6f 20 7a 65 72 6f 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 qual.to.zero..........Notes.....
6ba20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 44 69 72 69 63 68 6c 65 74 20 ....-----.........The.Dirichlet.
6ba40 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 20 61 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 6f distribution.is.a.distribution.o
6ba60 76 65 72 20 76 65 63 74 6f 72 73 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 78 60 20 74 68 ver.vectors.........:math:`x`.th
6ba80 61 74 20 66 75 6c 66 69 6c 20 74 68 65 20 63 6f 6e 64 69 74 69 6f 6e 73 20 3a 6d 61 74 68 3a 60 at.fulfil.the.conditions.:math:`
6baa0 78 5f 69 3e 30 60 20 61 6e 64 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 5c 73 75 6d 5f 7b x_i>0`.and.........:math:`\sum_{
6bac0 69 3d 31 7d 5e 6b 20 78 5f 69 20 3d 20 31 60 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 i=1}^k.x_i.=.1`...........The.pr
6bae0 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 20 3a 6d 61 74 68 obability.density.function.:math
6bb00 3a 60 70 60 20 6f 66 20 61 0a 20 20 20 20 20 20 20 20 44 69 72 69 63 68 6c 65 74 2d 64 69 73 74 :`p`.of.a.........Dirichlet-dist
6bb20 72 69 62 75 74 65 64 20 72 61 6e 64 6f 6d 20 76 65 63 74 6f 72 20 3a 6d 61 74 68 3a 60 58 60 20 ributed.random.vector.:math:`X`.
6bb40 69 73 0a 20 20 20 20 20 20 20 20 70 72 6f 70 6f 72 74 69 6f 6e 61 6c 20 74 6f 0a 0a 20 20 20 20 is.........proportional.to......
6bb60 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 5c 70 72 6f 70 74 6f 20 5c 70 72 6f 64 .......math::.p(x).\propto.\prod
6bb80 5f 7b 69 3d 31 7d 5e 7b 6b 7d 7b 78 5e 7b 5c 61 6c 70 68 61 5f 69 2d 31 7d 5f 69 7d 2c 0a 0a 20 _{i=1}^{k}{x^{\alpha_i-1}_i},...
6bba0 20 20 20 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 5c 61 6c 70 68 61 60 20 69 73 20 61 .......where.:math:`\alpha`.is.a
6bbc0 20 76 65 63 74 6f 72 20 63 6f 6e 74 61 69 6e 69 6e 67 20 74 68 65 20 70 6f 73 69 74 69 76 65 0a .vector.containing.the.positive.
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6bc00 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 6d 65 74 68 6f 64 20 75 73 65 73 20 74 68 65 20 66 ...........The.method.uses.the.f
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6bd40 4d 63 4b 61 79 2c 20 22 49 6e 66 6f 72 6d 61 74 69 6f 6e 20 54 68 65 6f 72 79 2c 20 49 6e 66 65 McKay,."Information.Theory,.Infe
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6cf80 6f 6e 73 68 69 70 20 74 6f 0a 20 20 20 20 20 20 20 20 42 72 6f 77 6e 69 61 6e 20 6d 6f 74 69 6f onship.to.........Brownian.motio
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6cfe0 20 62 65 63 61 75 73 65 20 74 68 65 72 65 20 69 73 20 61 6e 20 69 6e 76 65 72 73 65 20 72 65 6c .because.there.is.an.inverse.rel
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6d480 77 6e 69 61 6e 20 6d 6f 74 69 6f 6e 2e 20 49 74 20 69 73 20 61 6c 73 6f 20 61 0a 20 20 20 20 20 wnian.motion..It.is.also.a......
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6d500 61 6e 64 20 69 6e 74 65 72 65 73 74 20 72 61 74 65 20 70 72 6f 63 65 73 73 65 73 2e 0a 0a 20 20 and.interest.rate.processes.....
6d520 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d ......References.........-------
6d540 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 42 72 69 67 68 74 6f 6e 20 57 65 62 73 ---............[1].Brighton.Webs
6d560 20 4c 74 64 2e 2c 20 57 61 6c 64 20 44 69 73 74 72 69 62 75 74 69 6f 6e 2c 0a 20 20 20 20 20 20 .Ltd.,.Wald.Distribution,.......
6d580 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 77 65 62 2e 61 72 63 68 69 76 65 2e 6f 72 67 .........https://web.archive.org
6d5a0 2f 77 65 62 2f 32 30 30 39 30 34 32 33 30 31 34 30 31 30 2f 68 74 74 70 3a 2f 2f 77 77 77 2e 62 /web/20090423014010/http://www.b
6d5c0 72 69 67 68 74 6f 6e 2d 77 65 62 73 2e 63 6f 2e 75 6b 3a 38 30 2f 64 69 73 74 72 69 62 75 74 69 righton-webs.co.uk:80/distributi
6d5e0 6f 6e 73 2f 77 61 6c 64 2e 61 73 70 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 43 68 68 69 ons/wald.asp............[2].Chhi
6d600 6b 61 72 61 2c 20 52 61 6a 20 53 2e 2c 20 61 6e 64 20 46 6f 6c 6b 73 2c 20 4a 2e 20 4c 65 72 6f kara,.Raj.S.,.and.Folks,.J..Lero
6d620 79 2c 20 22 54 68 65 20 49 6e 76 65 72 73 65 20 47 61 75 73 73 69 61 6e 0a 20 20 20 20 20 20 20 y,."The.Inverse.Gaussian........
6d640 20 20 20 20 20 20 20 20 44 69 73 74 72 69 62 75 74 69 6f 6e 3a 20 54 68 65 6f 72 79 20 3a 20 4d ........Distribution:.Theory.:.M
6d660 65 74 68 6f 64 6f 6c 6f 67 79 2c 20 61 6e 64 20 41 70 70 6c 69 63 61 74 69 6f 6e 73 22 2c 20 43 ethodology,.and.Applications",.C
6d680 52 43 20 50 72 65 73 73 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 31 39 38 38 2e 0a 20 RC.Press,................1988...
6d6a0 20 20 20 20 20 20 20 2e 2e 20 5b 33 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 49 6e 76 65 72 73 ..........[3].Wikipedia,."Invers
6d6c0 65 20 47 61 75 73 73 69 61 6e 20 64 69 73 74 72 69 62 75 74 69 6f 6e 22 0a 20 20 20 20 20 20 20 e.Gaussian.distribution"........
6d6e0 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 ........https://en.wikipedia.org
6d700 2f 77 69 6b 69 2f 49 6e 76 65 72 73 65 5f 47 61 75 73 73 69 61 6e 5f 64 69 73 74 72 69 62 75 74 /wiki/Inverse_Gaussian_distribut
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6d740 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 76 61 6c 75 65 73 20 66 72 6f 6d 20 ------.........Draw.values.from.
6d760 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 61 6e 64 20 70 6c 6f 74 20 74 68 65 20 68 69 the.distribution.and.plot.the.hi
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6d7a0 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e plotlib.pyplot.as.plt.........>>
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6dd80 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d ..........Examples.........-----
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703a0 20 20 20 20 49 66 20 61 72 72 61 79 2d 6c 69 6b 65 2c 20 6d 75 73 74 20 63 6f 6e 74 61 69 6e 20 ....If.array-like,.must.contain.
703c0 69 6e 74 65 67 65 72 20 76 61 6c 75 65 73 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e integer.values.........size.:.in
703e0 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 t.or.tuple.of.ints,.optional....
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70440 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b ``,.then.............``m.*.n.*.k
70460 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 44 65 66 61 75 6c 74 20 69 ``.samples.are.drawn...Default.i
70480 73 20 4e 6f 6e 65 2c 20 69 6e 20 77 68 69 63 68 20 63 61 73 65 20 61 0a 20 20 20 20 20 20 20 20 s.None,.in.which.case.a.........
704a0 20 20 20 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 2e 0a 20 20 ....single.value.is.returned....
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704e0 20 20 20 20 20 20 20 20 20 20 44 65 73 69 72 65 64 20 64 74 79 70 65 20 6f 66 20 74 68 65 20 72 ..........Desired.dtype.of.the.r
70500 65 73 75 6c 74 2e 20 42 79 74 65 6f 72 64 65 72 20 6d 75 73 74 20 62 65 20 6e 61 74 69 76 65 2e esult..Byteorder.must.be.native.
70520 0a 20 20 20 20 20 20 20 20 20 20 20 20 54 68 65 20 64 65 66 61 75 6c 74 20 76 61 6c 75 65 20 69 .............The.default.value.i
70540 73 20 6e 70 2e 69 6e 74 36 34 2e 0a 20 20 20 20 20 20 20 20 65 6e 64 70 6f 69 6e 74 20 3a 20 62 s.np.int64..........endpoint.:.b
70560 6f 6f 6c 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 74 72 75 ool,.optional.............If.tru
70580 65 2c 20 73 61 6d 70 6c 65 20 66 72 6f 6d 20 74 68 65 20 69 6e 74 65 72 76 61 6c 20 5b 6c 6f 77 e,.sample.from.the.interval.[low
705a0 2c 20 68 69 67 68 5d 20 69 6e 73 74 65 61 64 20 6f 66 20 74 68 65 0a 20 20 20 20 20 20 20 20 20 ,.high].instead.of.the..........
705c0 20 20 20 64 65 66 61 75 6c 74 20 5b 6c 6f 77 2c 20 68 69 67 68 29 0a 20 20 20 20 20 20 20 20 20 ...default.[low,.high)..........
705e0 20 20 20 44 65 66 61 75 6c 74 73 20 74 6f 20 46 61 6c 73 65 0a 0a 20 20 20 20 20 20 20 20 52 65 ...Defaults.to.False..........Re
70600 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 turns.........-------.........ou
70620 74 20 3a 20 69 6e 74 20 6f 72 20 6e 64 61 72 72 61 79 20 6f 66 20 69 6e 74 73 0a 20 20 20 20 20 t.:.int.or.ndarray.of.ints......
70640 20 20 20 20 20 20 20 60 73 69 7a 65 60 2d 73 68 61 70 65 64 20 61 72 72 61 79 20 6f 66 20 72 61 .......`size`-shaped.array.of.ra
70660 6e 64 6f 6d 20 69 6e 74 65 67 65 72 73 20 66 72 6f 6d 20 74 68 65 20 61 70 70 72 6f 70 72 69 61 ndom.integers.from.the.appropria
70680 74 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 20 6f 72 20 te.............distribution,.or.
706a0 61 20 73 69 6e 67 6c 65 20 73 75 63 68 20 72 61 6e 64 6f 6d 20 69 6e 74 20 69 66 20 60 73 69 7a a.single.such.random.int.if.`siz
706c0 65 60 20 6e 6f 74 20 70 72 6f 76 69 64 65 64 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a e`.not.provided...........Notes.
706e0 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 57 68 65 6e 20 75 73 69 6e 67 ........-----.........When.using
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70740 20 20 20 20 63 61 6e 6e 6f 74 20 62 65 20 72 65 70 72 65 73 65 6e 74 65 64 20 61 73 20 61 20 73 ....cannot.be.represented.as.a.s
70760 74 61 6e 64 61 72 64 20 69 6e 74 65 67 65 72 20 74 79 70 65 2e 20 54 68 65 20 68 69 67 68 20 61 tandard.integer.type..The.high.a
70780 72 72 61 79 20 28 6f 72 0a 20 20 20 20 20 20 20 20 6c 6f 77 20 69 66 20 68 69 67 68 20 69 73 20 rray.(or.........low.if.high.is.
707a0 4e 6f 6e 65 29 20 6d 75 73 74 20 68 61 76 65 20 6f 62 6a 65 63 74 20 64 74 79 70 65 2c 20 65 2e None).must.have.object.dtype,.e.
707c0 67 2e 2c 20 61 72 72 61 79 28 5b 32 2a 2a 36 34 5d 29 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 g.,.array([2**64])...........Exa
707e0 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 3e mples.........--------.........>
70800 3e 3e 20 72 6e 67 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 >>.rng.=.np.random.default_rng()
70820 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 32 2c 20 73 69 7a .........>>>.rng.integers(2,.siz
70840 65 3d 31 30 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 31 2c 20 30 2c 20 30 2c 20 30 2c e=10).........array([1,.0,.0,.0,
70860 20 31 2c 20 31 2c 20 30 2c 20 30 2c 20 31 2c 20 30 5d 29 20 20 23 20 72 61 6e 64 6f 6d 0a 20 20 .1,.1,.0,.0,.1,.0])..#.random...
70880 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 31 2c 20 73 69 7a 65 3d 31 ......>>>.rng.integers(1,.size=1
708a0 30 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 30 2c 20 30 2c 20 30 2c 20 30 2c 20 30 2c 0).........array([0,.0,.0,.0,.0,
708c0 20 30 2c 20 30 2c 20 30 2c 20 30 2c 20 30 5d 29 0a 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 .0,.0,.0,.0,.0])..........Genera
708e0 74 65 20 61 20 32 20 78 20 34 20 61 72 72 61 79 20 6f 66 20 69 6e 74 73 20 62 65 74 77 65 65 6e te.a.2.x.4.array.of.ints.between
70900 20 30 20 61 6e 64 20 34 2c 20 69 6e 63 6c 75 73 69 76 65 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e .0.and.4,.inclusive:..........>>
70920 3e 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 35 2c 20 73 69 7a 65 3d 28 32 2c 20 34 29 29 0a 20 >.rng.integers(5,.size=(2,.4))..
70940 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 5b 34 2c 20 30 2c 20 32 2c 20 31 5d 2c 0a 20 20 20 20 .......array([[4,.0,.2,.1],.....
70960 20 20 20 20 20 20 20 20 20 20 20 5b 33 2c 20 32 2c 20 32 2c 20 30 5d 5d 29 20 20 23 20 72 61 6e ...........[3,.2,.2,.0]])..#.ran
70980 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 74 65 20 61 20 31 20 78 20 33 20 61 72 dom..........Generate.a.1.x.3.ar
709a0 72 61 79 20 77 69 74 68 20 33 20 64 69 66 66 65 72 65 6e 74 20 75 70 70 65 72 20 62 6f 75 6e 64 ray.with.3.different.upper.bound
709c0 73 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 31 2c 20 5b s..........>>>.rng.integers(1,.[
709e0 33 2c 20 35 2c 20 31 30 5d 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 32 2c 20 32 2c 20 3,.5,.10]).........array([2,.2,.
70a00 39 5d 29 20 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 74 65 20 9])..#.random..........Generate.
70a20 61 20 31 20 62 79 20 33 20 61 72 72 61 79 20 77 69 74 68 20 33 20 64 69 66 66 65 72 65 6e 74 20 a.1.by.3.array.with.3.different.
70a40 6c 6f 77 65 72 20 62 6f 75 6e 64 73 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 69 6e lower.bounds..........>>>.rng.in
70a60 74 65 67 65 72 73 28 5b 31 2c 20 35 2c 20 37 5d 2c 20 31 30 29 0a 20 20 20 20 20 20 20 20 61 72 tegers([1,.5,.7],.10).........ar
70a80 72 61 79 28 5b 39 2c 20 38 2c 20 37 5d 29 20 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 ray([9,.8,.7])..#.random........
70aa0 20 20 47 65 6e 65 72 61 74 65 20 61 20 32 20 62 79 20 34 20 61 72 72 61 79 20 75 73 69 6e 67 20 ..Generate.a.2.by.4.array.using.
70ac0 62 72 6f 61 64 63 61 73 74 69 6e 67 20 77 69 74 68 20 64 74 79 70 65 20 6f 66 20 75 69 6e 74 38 broadcasting.with.dtype.of.uint8
70ae0 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 5b 31 2c 20 33 ..........>>>.rng.integers([1,.3
70b00 2c 20 35 2c 20 37 5d 2c 20 5b 5b 31 30 5d 2c 20 5b 32 30 5d 5d 2c 20 64 74 79 70 65 3d 6e 70 2e ,.5,.7],.[[10],.[20]],.dtype=np.
70b20 75 69 6e 74 38 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 5b 20 38 2c 20 20 36 2c 20 20 uint8).........array([[.8,..6,..
70b40 39 2c 20 20 37 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5b 20 31 2c 20 31 36 2c 20 9,..7],................[.1,.16,.
70b60 20 39 2c 20 31 32 5d 5d 2c 20 64 74 79 70 65 3d 75 69 6e 74 38 29 20 20 23 20 72 61 6e 64 6f 6d .9,.12]],.dtype=uint8)..#.random
70b80 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d ..........References.........---
70ba0 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 44 61 6e 69 65 6c 20 4c 65 -------............[1].Daniel.Le
70bc0 6d 69 72 65 2e 2c 20 22 46 61 73 74 20 52 61 6e 64 6f 6d 20 49 6e 74 65 67 65 72 20 47 65 6e 65 mire.,."Fast.Random.Integer.Gene
70be0 72 61 74 69 6f 6e 20 69 6e 20 61 6e 20 49 6e 74 65 72 76 61 6c 22 2c 0a 20 20 20 20 20 20 20 20 ration.in.an.Interval",.........
70c00 20 20 20 20 20 20 20 41 43 4d 20 54 72 61 6e 73 61 63 74 69 6f 6e 73 20 6f 6e 20 4d 6f 64 65 6c .......ACM.Transactions.on.Model
70c20 69 6e 67 20 61 6e 64 20 43 6f 6d 70 75 74 65 72 20 53 69 6d 75 6c 61 74 69 6f 6e 20 32 39 20 28 ing.and.Computer.Simulation.29.(
70c40 31 29 2c 20 32 30 31 39 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 1),.2019,................http://
70c60 61 72 78 69 76 2e 6f 72 67 2f 61 62 73 2f 31 38 30 35 2e 31 30 39 34 31 2e 0a 0a 20 20 20 20 20 arxiv.org/abs/1805.10941........
70c80 20 20 20 00 6c 65 66 74 00 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 6c 6f 67 6e 6f 72 6d ....left.................lognorm
70ca0 61 6c 28 6d 65 61 6e 3d 30 2e 30 2c 20 73 69 67 6d 61 3d 31 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e al(mean=0.0,.sigma=1.0,.size=Non
70cc0 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 e)..........Draw.samples.from.a.
70ce0 6c 6f 67 2d 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 log-normal.distribution.........
70d00 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 6c 6f 67 2d 6e 6f 72 6d 61 6c ..Draw.samples.from.a.log-normal
70d20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 77 69 74 68 20 73 70 65 63 69 66 69 65 64 20 6d 65 61 .distribution.with.specified.mea
70d40 6e 2c 0a 20 20 20 20 20 20 20 20 73 74 61 6e 64 61 72 64 20 64 65 76 69 61 74 69 6f 6e 2c 20 61 n,.........standard.deviation,.a
70d60 6e 64 20 61 72 72 61 79 20 73 68 61 70 65 2e 20 20 4e 6f 74 65 20 74 68 61 74 20 74 68 65 20 6d nd.array.shape...Note.that.the.m
70d80 65 61 6e 20 61 6e 64 20 73 74 61 6e 64 61 72 64 0a 20 20 20 20 20 20 20 20 64 65 76 69 61 74 69 ean.and.standard.........deviati
70da0 6f 6e 20 61 72 65 20 6e 6f 74 20 74 68 65 20 76 61 6c 75 65 73 20 66 6f 72 20 74 68 65 20 64 69 on.are.not.the.values.for.the.di
70dc0 73 74 72 69 62 75 74 69 6f 6e 20 69 74 73 65 6c 66 2c 20 62 75 74 20 6f 66 20 74 68 65 0a 20 20 stribution.itself,.but.of.the...
70de0 20 20 20 20 20 20 75 6e 64 65 72 6c 79 69 6e 67 20 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 ......underlying.normal.distribu
70e00 74 69 6f 6e 20 69 74 20 69 73 20 64 65 72 69 76 65 64 20 66 72 6f 6d 2e 0a 0a 20 20 20 20 20 20 tion.it.is.derived.from.........
70e20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a ..Parameters.........----------.
70e40 20 20 20 20 20 20 20 20 6d 65 61 6e 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 ........mean.:.float.or.array_li
70e60 6b 65 20 6f 66 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 ke.of.floats,.optional..........
70e80 20 20 20 4d 65 61 6e 20 76 61 6c 75 65 20 6f 66 20 74 68 65 20 75 6e 64 65 72 6c 79 69 6e 67 20 ...Mean.value.of.the.underlying.
70ea0 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 44 65 66 61 75 6c 74 20 69 73 20 normal.distribution..Default.is.
70ec0 30 2e 0a 20 20 20 20 20 20 20 20 73 69 67 6d 61 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 0..........sigma.:.float.or.arra
70ee0 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 y_like.of.floats,.optional......
70f00 20 20 20 20 20 20 20 53 74 61 6e 64 61 72 64 20 64 65 76 69 61 74 69 6f 6e 20 6f 66 20 74 68 65 .......Standard.deviation.of.the
70f20 20 75 6e 64 65 72 6c 79 69 6e 67 20 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e .underlying.normal.distribution.
70f40 20 4d 75 73 74 20 62 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 .Must.be.............non-negativ
70f60 65 2e 20 44 65 66 61 75 6c 74 20 69 73 20 31 2e 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 e..Default.is.1..........size.:.
70f80 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 int.or.tuple.of.ints,.optional..
70fa0 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 ...........Output.shape...If.the
70fc0 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 .given.shape.is,.e.g.,.``(m,.n,.
70fe0 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a k)``,.then.............``m.*.n.*
71000 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 .k``.samples.are.drawn...If.size
71020 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 20 20 20 20 20 .is.``None``.(default),.........
71040 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 ....a.single.value.is.returned.i
71060 66 20 60 60 6d 65 61 6e 60 60 20 61 6e 64 20 60 60 73 69 67 6d 61 60 60 20 61 72 65 20 62 6f 74 f.``mean``.and.``sigma``.are.bot
71080 68 20 73 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 68 65 72 77 69 73 65 h.scalars..............Otherwise
710a0 2c 20 60 60 6e 70 2e 62 72 6f 61 64 63 61 73 74 28 6d 65 61 6e 2c 20 73 69 67 6d 61 29 2e 73 69 ,.``np.broadcast(mean,.sigma).si
710c0 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 ze``.samples.are.drawn..........
710e0 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 .Returns.........-------........
71100 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 .out.:.ndarray.or.scalar........
71120 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 .....Drawn.samples.from.the.para
71140 6d 65 74 65 72 69 7a 65 64 20 6c 6f 67 2d 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f meterized.log-normal.distributio
71160 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d n...........See.Also.........---
71180 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 6c 6f 67 6e 6f 72 -----.........scipy.stats.lognor
711a0 6d 20 3a 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e m.:.probability.density.function
711c0 2c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 63 75 6d 75 ,.distribution,.............cumu
711e0 6c 61 74 69 76 65 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 65 74 63 2e 0a 0a 20 lative.density.function,.etc....
71200 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 .......Notes.........-----......
71220 20 20 20 41 20 76 61 72 69 61 62 6c 65 20 60 78 60 20 68 61 73 20 61 20 6c 6f 67 2d 6e 6f 72 6d ...A.variable.`x`.has.a.log-norm
71240 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 66 20 60 6c 6f 67 28 78 29 60 20 69 73 20 6e al.distribution.if.`log(x)`.is.n
71260 6f 72 6d 61 6c 6c 79 0a 20 20 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 65 64 2e 20 20 54 68 ormally.........distributed...Th
71280 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 20 66 e.probability.density.function.f
712a0 6f 72 20 74 68 65 20 6c 6f 67 2d 6e 6f 72 6d 61 6c 0a 20 20 20 20 20 20 20 20 64 69 73 74 72 69 or.the.log-normal.........distri
712c0 62 75 74 69 6f 6e 20 69 73 3a 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 bution.is:.............math::.p(
712e0 78 29 20 3d 20 5c 66 72 61 63 7b 31 7d 7b 5c 73 69 67 6d 61 20 78 20 5c 73 71 72 74 7b 32 5c 70 x).=.\frac{1}{\sigma.x.\sqrt{2\p
71300 69 7d 7d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 65 5e 7b i}}..........................e^{
71320 28 2d 5c 66 72 61 63 7b 28 6c 6e 28 78 29 2d 5c 6d 75 29 5e 32 7d 7b 32 5c 73 69 67 6d 61 5e 32 (-\frac{(ln(x)-\mu)^2}{2\sigma^2
71340 7d 29 7d 0a 0a 20 20 20 20 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 5c 6d 75 60 20 69 })}..........where.:math:`\mu`.i
71360 73 20 74 68 65 20 6d 65 61 6e 20 61 6e 64 20 3a 6d 61 74 68 3a 60 5c 73 69 67 6d 61 60 20 69 73 s.the.mean.and.:math:`\sigma`.is
71380 20 74 68 65 20 73 74 61 6e 64 61 72 64 0a 20 20 20 20 20 20 20 20 64 65 76 69 61 74 69 6f 6e 20 .the.standard.........deviation.
713a0 6f 66 20 74 68 65 20 6e 6f 72 6d 61 6c 6c 79 20 64 69 73 74 72 69 62 75 74 65 64 20 6c 6f 67 61 of.the.normally.distributed.loga
713c0 72 69 74 68 6d 20 6f 66 20 74 68 65 20 76 61 72 69 61 62 6c 65 2e 0a 20 20 20 20 20 20 20 20 41 rithm.of.the.variable..........A
713e0 20 6c 6f 67 2d 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 72 65 73 75 6c 74 73 .log-normal.distribution.results
71400 20 69 66 20 61 20 72 61 6e 64 6f 6d 20 76 61 72 69 61 62 6c 65 20 69 73 20 74 68 65 20 2a 70 72 .if.a.random.variable.is.the.*pr
71420 6f 64 75 63 74 2a 0a 20 20 20 20 20 20 20 20 6f 66 20 61 20 6c 61 72 67 65 20 6e 75 6d 62 65 72 oduct*.........of.a.large.number
71440 20 6f 66 20 69 6e 64 65 70 65 6e 64 65 6e 74 2c 20 69 64 65 6e 74 69 63 61 6c 6c 79 2d 64 69 73 .of.independent,.identically-dis
71460 74 72 69 62 75 74 65 64 20 76 61 72 69 61 62 6c 65 73 20 69 6e 0a 20 20 20 20 20 20 20 20 74 68 tributed.variables.in.........th
71480 65 20 73 61 6d 65 20 77 61 79 20 74 68 61 74 20 61 20 6e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 e.same.way.that.a.normal.distrib
714a0 75 74 69 6f 6e 20 72 65 73 75 6c 74 73 20 69 66 20 74 68 65 20 76 61 72 69 61 62 6c 65 20 69 73 ution.results.if.the.variable.is
714c0 20 74 68 65 0a 20 20 20 20 20 20 20 20 2a 73 75 6d 2a 20 6f 66 20 61 20 6c 61 72 67 65 20 6e 75 .the.........*sum*.of.a.large.nu
714e0 6d 62 65 72 20 6f 66 20 69 6e 64 65 70 65 6e 64 65 6e 74 2c 20 69 64 65 6e 74 69 63 61 6c 6c 79 mber.of.independent,.identically
71500 2d 64 69 73 74 72 69 62 75 74 65 64 0a 20 20 20 20 20 20 20 20 76 61 72 69 61 62 6c 65 73 2e 0a -distributed.........variables..
71520 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d .........References.........----
71540 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 4c 69 6d 70 65 72 74 2c 20 45 ------............[1].Limpert,.E
71560 2e 2c 20 53 74 61 68 65 6c 2c 20 57 2e 20 41 2e 2c 20 61 6e 64 20 41 62 62 74 2c 20 4d 2e 2c 20 .,.Stahel,.W..A.,.and.Abbt,.M.,.
71580 22 4c 6f 67 2d 6e 6f 72 6d 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 44 69 73 74 72 "Log-normal................Distr
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71660 52 2e 44 2e 20 61 6e 64 20 54 68 6f 6d 61 73 2c 20 4d 2e 2c 20 22 53 74 61 74 69 73 74 69 63 61 R.D..and.Thomas,.M.,."Statistica
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716c0 56 65 72 6c 61 67 2c 20 32 30 30 31 2c 20 70 70 2e 20 33 31 2d 33 32 2e 0a 0a 20 20 20 20 20 20 Verlag,.2001,.pp..31-32.........
716e0 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 ..Examples.........--------.....
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71740 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6d ndom.default_rng().........>>>.m
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71780 6e 64 61 72 64 20 64 65 76 69 61 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 ndard.deviation.........>>>.s.=.
717a0 72 6e 67 2e 6c 6f 67 6e 6f 72 6d 61 6c 28 6d 75 2c 20 73 69 67 6d 61 2c 20 31 30 30 30 29 0a 0a rng.lognormal(mu,.sigma,.1000)..
717c0 20 20 20 20 20 20 20 20 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 20 6f 66 ........Display.the.histogram.of
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71840 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 63 6f 75 6e b.pyplot.as.plt.........>>>.coun
71860 74 2c 20 62 69 6e 73 2c 20 69 67 6e 6f 72 65 64 20 3d 20 70 6c 74 2e 68 69 73 74 28 73 2c 20 31 t,.bins,.ignored.=.plt.hist(s,.1
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718a0 20 20 20 20 20 20 20 20 3e 3e 3e 20 78 20 3d 20 6e 70 2e 6c 69 6e 73 70 61 63 65 28 6d 69 6e 28 ........>>>.x.=.np.linspace(min(
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71900 20 6d 75 29 2a 2a 32 20 2f 20 28 32 20 2a 20 73 69 67 6d 61 2a 2a 32 29 29 0a 20 20 20 20 20 20 .mu)**2./.(2.*.sigma**2)).......
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71940 71 72 74 28 32 20 2a 20 6e 70 2e 70 69 29 29 29 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c qrt(2.*.np.pi)))..........>>>.pl
71960 74 2e 70 6c 6f 74 28 78 2c 20 70 64 66 2c 20 6c 69 6e 65 77 69 64 74 68 3d 32 2c 20 63 6f 6c 6f t.plot(x,.pdf,.linewidth=2,.colo
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719a0 68 74 27 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 ht').........>>>.plt.show().....
719c0 20 20 20 20 20 44 65 6d 6f 6e 73 74 72 61 74 65 20 74 68 61 74 20 74 61 6b 69 6e 67 20 74 68 65 .....Demonstrate.that.taking.the
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71a40 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 0a 20 20 20 20 20 20 20 20 66 75 6e 63 probability.density.........func
71a60 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 23 20 47 65 6e 65 72 61 74 65 20 61 20 tion...........>>>.#.Generate.a.
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71b80 28 6e 70 2e 70 72 6f 64 75 63 74 28 61 29 29 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 62 20 3d (np.product(a))..........>>>.b.=
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71c40 28 6e 70 2e 6c 6f 67 28 62 29 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6d 75 20 3d 20 6e 70 2e (np.log(b)).........>>>.mu.=.np.
71c60 6d 65 61 6e 28 6e 70 2e 6c 6f 67 28 62 29 29 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 78 20 3d mean(np.log(b))..........>>>.x.=
71c80 20 6e 70 2e 6c 69 6e 73 70 61 63 65 28 6d 69 6e 28 62 69 6e 73 29 2c 20 6d 61 78 28 62 69 6e 73 .np.linspace(min(bins),.max(bins
71ca0 29 2c 20 31 30 30 30 30 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 64 66 20 3d 20 28 6e 70 2e ),.10000).........>>>.pdf.=.(np.
71cc0 65 78 70 28 2d 28 6e 70 2e 6c 6f 67 28 78 29 20 2d 20 6d 75 29 2a 2a 32 20 2f 20 28 32 20 2a 20 exp(-(np.log(x).-.mu)**2./.(2.*.
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71d40 63 6f 6c 6f 72 3d 27 72 27 2c 20 6c 69 6e 65 77 69 64 74 68 3d 32 29 0a 20 20 20 20 20 20 20 20 color='r',.linewidth=2).........
71d60 3e 3e 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 20 20 20 00 00 00 00 00 00 00 00 >>>.plt.show()..................
71d80 73 75 6d 28 70 76 61 6c 73 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 73 74 61 6e 64 61 72 sum(pvals................standar
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71de0 27 73 20 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 77 69 74 68 20 60 64 66 60 20 64 65 67 72 's.t.distribution.with.`df`.degr
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71e20 20 41 20 73 70 65 63 69 61 6c 20 63 61 73 65 20 6f 66 20 74 68 65 20 68 79 70 65 72 62 6f 6c 69 .A.special.case.of.the.hyperboli
71e40 63 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 20 41 73 20 60 64 66 60 20 67 65 74 73 0a 20 20 c.distribution...As.`df`.gets...
71e60 20 20 20 20 20 20 6c 61 72 67 65 2c 20 74 68 65 20 72 65 73 75 6c 74 20 72 65 73 65 6d 62 6c 65 ......large,.the.result.resemble
71e80 73 20 74 68 61 74 20 6f 66 20 74 68 65 20 73 74 61 6e 64 61 72 64 20 6e 6f 72 6d 61 6c 0a 20 20 s.that.of.the.standard.normal...
71ea0 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 28 60 73 74 61 6e 64 61 72 64 5f 6e 6f ......distribution.(`standard_no
71ec0 72 6d 61 6c 60 29 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 rmal`)...........Parameters.....
71ee0 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 64 66 20 3a 20 66 6c 6f 61 ....----------.........df.:.floa
71f00 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 t.or.array_like.of.floats.......
71f20 20 20 20 20 20 20 44 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 2c 20 6d 75 73 74 20 62 ......Degrees.of.freedom,.must.b
71f40 65 20 3e 20 30 2e 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 e.>.0..........size.:.int.or.tup
71f60 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 le.of.ints,.optional............
71f80 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 .Output.shape...If.the.given.sha
71fa0 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e pe.is,.e.g.,.``(m,.n,.k)``,.then
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72080 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 s.are.drawn...........Returns...
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720c0 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 ray.or.scalar.............Drawn.
720e0 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 73 samples.from.the.parameterized.s
72100 74 61 6e 64 61 72 64 20 53 74 75 64 65 6e 74 27 73 20 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e tandard.Student's.t.distribution
72120 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 ...........Notes.........-----..
72140 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 .......The.probability.density.f
72160 75 6e 63 74 69 6f 6e 20 66 6f 72 20 74 68 65 20 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 unction.for.the.t.distribution.i
72180 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 50 28 78 2c 20 64 66 29 20 3d 20 s.............math::.P(x,.df).=.
721a0 5c 66 72 61 63 7b 5c 47 61 6d 6d 61 28 5c 66 72 61 63 7b 64 66 2b 31 7d 7b 32 7d 29 7d 7b 5c 73 \frac{\Gamma(\frac{df+1}{2})}{\s
721c0 71 72 74 7b 5c 70 69 20 64 66 7d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5c 47 qrt{\pi.df}...................\G
721e0 61 6d 6d 61 28 5c 66 72 61 63 7b 64 66 7d 7b 32 7d 29 7d 5c 42 69 67 6c 28 20 31 2b 5c 66 72 61 amma(\frac{df}{2})}\Bigl(.1+\fra
72200 63 7b 78 5e 32 7d 7b 64 66 7d 20 5c 42 69 67 72 29 5e 7b 2d 28 64 66 2b 31 29 2f 32 7d 0a 0a 20 c{x^2}{df}.\Bigr)^{-(df+1)/2}...
72220 20 20 20 20 20 20 20 54 68 65 20 74 20 74 65 73 74 20 69 73 20 62 61 73 65 64 20 6f 6e 20 61 6e .......The.t.test.is.based.on.an
72240 20 61 73 73 75 6d 70 74 69 6f 6e 20 74 68 61 74 20 74 68 65 20 64 61 74 61 20 63 6f 6d 65 20 66 .assumption.that.the.data.come.f
72260 72 6f 6d 20 61 0a 20 20 20 20 20 20 20 20 4e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f rom.a.........Normal.distributio
72280 6e 2e 20 54 68 65 20 74 20 74 65 73 74 20 70 72 6f 76 69 64 65 73 20 61 20 77 61 79 20 74 6f 20 n..The.t.test.provides.a.way.to.
722a0 74 65 73 74 20 77 68 65 74 68 65 72 0a 20 20 20 20 20 20 20 20 74 68 65 20 73 61 6d 70 6c 65 20 test.whether.........the.sample.
722c0 6d 65 61 6e 20 28 74 68 61 74 20 69 73 20 74 68 65 20 6d 65 61 6e 20 63 61 6c 63 75 6c 61 74 65 mean.(that.is.the.mean.calculate
722e0 64 20 66 72 6f 6d 20 74 68 65 20 64 61 74 61 29 20 69 73 0a 20 20 20 20 20 20 20 20 61 20 67 6f d.from.the.data).is.........a.go
72300 6f 64 20 65 73 74 69 6d 61 74 65 20 6f 66 20 74 68 65 20 74 72 75 65 20 6d 65 61 6e 2e 0a 0a 20 od.estimate.of.the.true.mean....
72320 20 20 20 20 20 20 20 54 68 65 20 64 65 72 69 76 61 74 69 6f 6e 20 6f 66 20 74 68 65 20 74 2d 64 .......The.derivation.of.the.t-d
72340 69 73 74 72 69 62 75 74 69 6f 6e 20 77 61 73 20 66 69 72 73 74 20 70 75 62 6c 69 73 68 65 64 20 istribution.was.first.published.
72360 69 6e 0a 20 20 20 20 20 20 20 20 31 39 30 38 20 62 79 20 57 69 6c 6c 69 61 6d 20 47 6f 73 73 65 in.........1908.by.William.Gosse
72380 74 20 77 68 69 6c 65 20 77 6f 72 6b 69 6e 67 20 66 6f 72 20 74 68 65 20 47 75 69 6e 6e 65 73 73 t.while.working.for.the.Guinness
723a0 20 42 72 65 77 65 72 79 0a 20 20 20 20 20 20 20 20 69 6e 20 44 75 62 6c 69 6e 2e 20 44 75 65 20 .Brewery.........in.Dublin..Due.
723c0 74 6f 20 70 72 6f 70 72 69 65 74 61 72 79 20 69 73 73 75 65 73 2c 20 68 65 20 68 61 64 20 74 6f to.proprietary.issues,.he.had.to
723e0 20 70 75 62 6c 69 73 68 20 75 6e 64 65 72 0a 20 20 20 20 20 20 20 20 61 20 70 73 65 75 64 6f 6e .publish.under.........a.pseudon
72400 79 6d 2c 20 61 6e 64 20 73 6f 20 68 65 20 75 73 65 64 20 74 68 65 20 6e 61 6d 65 20 53 74 75 64 ym,.and.so.he.used.the.name.Stud
72420 65 6e 74 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 ent...........References........
72440 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 44 61 6c 67 61 .----------............[1].Dalga
72460 61 72 64 2c 20 50 65 74 65 72 2c 20 22 49 6e 74 72 6f 64 75 63 74 6f 72 79 20 53 74 61 74 69 73 ard,.Peter,."Introductory.Statis
72480 74 69 63 73 20 57 69 74 68 20 52 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 53 70 72 tics.With.R",................Spr
724a0 69 6e 67 65 72 2c 20 32 30 30 32 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 69 6b 69 inger,.2002.............[2].Wiki
724c0 70 65 64 69 61 2c 20 22 53 74 75 64 65 6e 74 27 73 20 74 2d 64 69 73 74 72 69 62 75 74 69 6f 6e pedia,."Student's.t-distribution
724e0 22 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 "................https://en.wiki
72500 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 53 74 75 64 65 6e 74 27 73 5f 74 2d 64 69 73 74 72 pedia.org/wiki/Student's_t-distr
72520 69 62 75 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 ibution..........Examples.......
72540 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 46 72 6f 6d 20 44 61 6c 67 61 61 72 64 ..--------.........From.Dalgaard
72560 20 70 61 67 65 20 38 33 20 5b 31 5d 5f 2c 20 73 75 70 70 6f 73 65 20 74 68 65 20 64 61 69 6c 79 .page.83.[1]_,.suppose.the.daily
72580 20 65 6e 65 72 67 79 20 69 6e 74 61 6b 65 20 66 6f 72 20 31 31 0a 20 20 20 20 20 20 20 20 77 6f .energy.intake.for.11.........wo
725a0 6d 65 6e 20 69 6e 20 6b 69 6c 6f 6a 6f 75 6c 65 73 20 28 6b 4a 29 20 69 73 3a 0a 0a 20 20 20 20 men.in.kilojoules.(kJ).is:......
725c0 20 20 20 20 3e 3e 3e 20 69 6e 74 61 6b 65 20 3d 20 6e 70 2e 61 72 72 61 79 28 5b 35 32 36 30 2e ....>>>.intake.=.np.array([5260.
725e0 2c 20 35 34 37 30 2c 20 35 36 34 30 2c 20 36 31 38 30 2c 20 36 33 39 30 2c 20 36 35 31 35 2c 20 ,.5470,.5640,.6180,.6390,.6515,.
72600 36 38 30 35 2c 20 37 35 31 35 2c 20 5c 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 20 20 6805,.7515,.\...................
72620 20 20 20 20 20 20 20 20 20 20 20 20 20 37 35 31 35 2c 20 38 32 33 30 2c 20 38 37 37 30 5d 29 0a .............7515,.8230,.8770]).
72640 0a 20 20 20 20 20 20 20 20 44 6f 65 73 20 74 68 65 69 72 20 65 6e 65 72 67 79 20 69 6e 74 61 6b .........Does.their.energy.intak
72660 65 20 64 65 76 69 61 74 65 20 73 79 73 74 65 6d 61 74 69 63 61 6c 6c 79 20 66 72 6f 6d 20 74 68 e.deviate.systematically.from.th
72680 65 20 72 65 63 6f 6d 6d 65 6e 64 65 64 0a 20 20 20 20 20 20 20 20 76 61 6c 75 65 20 6f 66 20 37 e.recommended.........value.of.7
726a0 37 32 35 20 6b 4a 3f 20 4f 75 72 20 6e 75 6c 6c 20 68 79 70 6f 74 68 65 73 69 73 20 77 69 6c 6c 725.kJ?.Our.null.hypothesis.will
726c0 20 62 65 20 74 68 65 20 61 62 73 65 6e 63 65 20 6f 66 20 64 65 76 69 61 74 69 6f 6e 2c 0a 20 20 .be.the.absence.of.deviation,...
726e0 20 20 20 20 20 20 61 6e 64 20 74 68 65 20 61 6c 74 65 72 6e 61 74 65 20 68 79 70 6f 74 68 65 73 ......and.the.alternate.hypothes
72700 69 73 20 77 69 6c 6c 20 62 65 20 74 68 65 20 70 72 65 73 65 6e 63 65 20 6f 66 20 61 6e 20 65 66 is.will.be.the.presence.of.an.ef
72720 66 65 63 74 20 74 68 61 74 20 63 6f 75 6c 64 20 62 65 0a 20 20 20 20 20 20 20 20 65 69 74 68 65 fect.that.could.be.........eithe
72740 72 20 70 6f 73 69 74 69 76 65 20 6f 72 20 6e 65 67 61 74 69 76 65 2c 20 68 65 6e 63 65 20 6d 61 r.positive.or.negative,.hence.ma
72760 6b 69 6e 67 20 6f 75 72 20 74 65 73 74 20 32 2d 74 61 69 6c 65 64 2e 20 0a 0a 20 20 20 20 20 20 king.our.test.2-tailed..........
72780 20 20 42 65 63 61 75 73 65 20 77 65 20 61 72 65 20 65 73 74 69 6d 61 74 69 6e 67 20 74 68 65 20 ..Because.we.are.estimating.the.
727a0 6d 65 61 6e 20 61 6e 64 20 77 65 20 68 61 76 65 20 4e 3d 31 31 20 76 61 6c 75 65 73 20 69 6e 20 mean.and.we.have.N=11.values.in.
727c0 6f 75 72 20 73 61 6d 70 6c 65 2c 0a 20 20 20 20 20 20 20 20 77 65 20 68 61 76 65 20 4e 2d 31 3d our.sample,.........we.have.N-1=
727e0 31 30 20 64 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 2e 20 57 65 20 73 65 74 20 6f 75 10.degrees.of.freedom..We.set.ou
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72820 0a 20 20 20 20 20 20 20 20 63 6f 6d 70 75 74 65 20 74 68 65 20 74 20 73 74 61 74 69 73 74 69 63 .........compute.the.t.statistic
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72860 70 69 72 69 63 61 6c 20 73 74 61 6e 64 61 72 64 20 0a 20 20 20 20 20 20 20 20 64 65 76 69 61 74 pirical.standard..........deviat
72880 69 6f 6e 20 6f 66 20 6f 75 72 20 69 6e 74 61 6b 65 2e 20 57 65 20 75 73 65 20 61 20 64 64 6f 66 ion.of.our.intake..We.use.a.ddof
728a0 20 6f 66 20 31 20 74 6f 20 62 61 73 65 20 74 68 65 20 63 6f 6d 70 75 74 61 74 69 6f 6e 20 6f 66 .of.1.to.base.the.computation.of
728c0 20 6f 75 72 20 0a 20 20 20 20 20 20 20 20 65 6d 70 69 72 69 63 61 6c 20 73 74 61 6e 64 61 72 64 .our..........empirical.standard
728e0 20 64 65 76 69 61 74 69 6f 6e 20 6f 6e 20 61 6e 20 75 6e 62 69 61 73 65 64 20 65 73 74 69 6d 61 .deviation.on.an.unbiased.estima
72900 74 65 20 6f 66 20 74 68 65 20 76 61 72 69 61 6e 63 65 20 28 6e 6f 74 65 3a 0a 20 20 20 20 20 20 te.of.the.variance.(note:.......
72920 20 20 74 68 65 20 66 69 6e 61 6c 20 65 73 74 69 6d 61 74 65 20 69 73 20 6e 6f 74 20 75 6e 62 69 ..the.final.estimate.is.not.unbi
72940 61 73 65 64 20 64 75 65 20 74 6f 20 74 68 65 20 63 6f 6e 63 61 76 65 20 6e 61 74 75 72 65 20 6f ased.due.to.the.concave.nature.o
72960 66 20 74 68 65 20 73 71 75 61 72 65 20 0a 20 20 20 20 20 20 20 20 72 6f 6f 74 29 2e 0a 0a 20 20 f.the.square..........root).....
72980 20 20 20 20 20 20 3e 3e 3e 20 6e 70 2e 6d 65 61 6e 28 69 6e 74 61 6b 65 29 0a 20 20 20 20 20 20 ......>>>.np.mean(intake).......
729a0 20 20 36 37 35 33 2e 36 33 36 33 36 33 36 33 36 33 36 34 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 ..6753.636363636364.........>>>.
729c0 69 6e 74 61 6b 65 2e 73 74 64 28 64 64 6f 66 3d 31 29 0a 20 20 20 20 20 20 20 20 31 31 34 32 2e intake.std(ddof=1).........1142.
729e0 31 32 33 32 32 32 31 33 37 33 37 32 37 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 74 20 3d 20 28 6e 1232221373727.........>>>.t.=.(n
72a00 70 2e 6d 65 61 6e 28 69 6e 74 61 6b 65 29 2d 37 37 32 35 29 2f 28 69 6e 74 61 6b 65 2e 73 74 64 p.mean(intake)-7725)/(intake.std
72a20 28 64 64 6f 66 3d 31 29 2f 6e 70 2e 73 71 72 74 28 6c 65 6e 28 69 6e 74 61 6b 65 29 29 29 0a 20 (ddof=1)/np.sqrt(len(intake)))..
72a40 20 20 20 20 20 20 20 3e 3e 3e 20 74 0a 20 20 20 20 20 20 20 20 2d 32 2e 38 32 30 37 35 34 30 36 .......>>>.t.........-2.82075406
72a60 30 38 33 31 30 31 39 38 0a 0a 20 20 20 20 20 20 20 20 57 65 20 64 72 61 77 20 31 30 30 30 30 30 08310198..........We.draw.100000
72a80 30 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 53 74 75 64 65 6e 74 27 73 20 74 20 64 69 73 74 72 0.samples.from.Student's.t.distr
72aa0 69 62 75 74 69 6f 6e 20 77 69 74 68 20 74 68 65 20 61 64 65 71 75 61 74 65 0a 20 20 20 20 20 20 ibution.with.the.adequate.......
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72ae0 3e 3e 20 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 >>.import.matplotlib.pyplot.as.p
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72b80 20 20 20 20 20 44 6f 65 73 20 6f 75 72 20 74 20 73 74 61 74 69 73 74 69 63 20 6c 61 6e 64 20 69 .....Does.our.t.statistic.land.i
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72bc0 73 20 66 6f 75 6e 64 20 61 74 20 0a 20 20 20 20 20 20 20 20 62 6f 74 68 20 74 61 69 6c 73 20 6f s.found.at..........both.tails.o
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72c20 20 66 6c 6f 61 74 28 6c 65 6e 28 73 29 29 0a 20 20 20 20 20 20 20 20 30 2e 30 31 38 33 31 38 20 .float(len(s)).........0.018318.
72c40 20 23 72 61 6e 64 6f 6d 20 3c 20 30 2e 30 35 2c 20 73 74 61 74 69 73 74 69 63 20 69 73 20 69 6e .#random.<.0.05,.statistic.is.in
72c60 20 63 72 69 74 69 63 61 6c 20 72 65 67 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 .critical.region..........The.pr
72c80 6f 62 61 62 69 6c 69 74 79 20 76 61 6c 75 65 20 66 6f 72 20 74 68 69 73 20 32 2d 74 61 69 6c 65 obability.value.for.this.2-taile
72ca0 64 20 74 65 73 74 20 69 73 20 61 62 6f 75 74 20 31 2e 38 33 25 2c 20 77 68 69 63 68 20 69 73 20 d.test.is.about.1.83%,.which.is.
72cc0 0a 20 20 20 20 20 20 20 20 6c 6f 77 65 72 20 74 68 61 6e 20 74 68 65 20 35 25 20 70 72 65 2d 64 .........lower.than.the.5%.pre-d
72ce0 65 74 65 72 6d 69 6e 65 64 20 73 69 67 6e 69 66 69 63 61 6e 63 65 20 74 68 72 65 73 68 6f 6c 64 etermined.significance.threshold
72d00 2e 20 0a 0a 20 20 20 20 20 20 20 20 54 68 65 72 65 66 6f 72 65 2c 20 74 68 65 20 70 72 6f 62 61 ............Therefore,.the.proba
72d20 62 69 6c 69 74 79 20 6f 66 20 6f 62 73 65 72 76 69 6e 67 20 76 61 6c 75 65 73 20 61 73 20 65 78 bility.of.observing.values.as.ex
72d40 74 72 65 6d 65 20 61 73 20 6f 75 72 20 69 6e 74 61 6b 65 0a 20 20 20 20 20 20 20 20 63 6f 6e 64 treme.as.our.intake.........cond
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72d80 20 62 65 69 6e 67 20 74 72 75 65 20 69 73 20 74 6f 6f 20 6c 6f 77 2c 20 61 6e 64 20 77 65 20 72 .being.true.is.too.low,.and.we.r
72da0 65 6a 65 63 74 20 0a 20 20 20 20 20 20 20 20 74 68 65 20 6e 75 6c 6c 20 68 79 70 6f 74 68 65 73 eject..........the.null.hypothes
72dc0 69 73 20 6f 66 20 6e 6f 20 64 65 76 69 61 74 69 6f 6e 2e 20 0a 0a 20 20 20 20 20 20 20 20 00 00 is.of.no.deviation..............
72de0 45 6c 6c 69 70 73 69 73 00 00 00 00 64 74 79 70 65 00 00 00 75 6e 70 61 63 6b 00 00 64 66 6e 75 Ellipsis....dtype...unpack..dfnu
72e00 6d 00 00 00 00 00 00 00 42 75 66 66 65 72 20 76 69 65 77 20 64 6f 65 73 20 6e 6f 74 20 65 78 70 m.......Buffer.view.does.not.exp
72e20 6f 73 65 20 73 74 72 69 64 65 73 00 00 00 00 00 52 61 6e 67 65 20 65 78 63 65 65 64 73 20 76 61 ose.strides.....Range.exceeds.va
72e40 6c 69 64 20 62 6f 75 6e 64 73 00 00 00 00 00 00 55 6e 73 75 70 70 6f 72 74 65 64 20 64 74 79 70 lid.bounds......Unsupported.dtyp
72e60 65 20 25 72 20 66 6f 72 20 73 74 61 6e 64 61 72 64 5f 67 61 6d 6d 61 00 62 61 73 65 00 00 00 00 e.%r.for.standard_gamma.base....
72e80 0a 20 20 20 20 20 20 20 20 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 28 6e 67 6f 6f 64 2c 20 6e .........hypergeometric(ngood,.n
72ea0 62 61 64 2c 20 6e 73 61 6d 70 6c 65 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 bad,.nsample,.size=None)........
72ec0 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 48 79 70 65 72 67 65 6f 6d 65 ..Draw.samples.from.a.Hypergeome
72ee0 74 72 69 63 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 61 6d 70 tric.distribution...........Samp
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72f40 20 20 20 20 20 20 20 20 70 61 72 61 6d 65 74 65 72 73 2c 20 60 6e 67 6f 6f 64 60 20 28 77 61 79 ........parameters,.`ngood`.(way
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72fa0 73 65 6c 65 63 74 69 6f 6e 29 2c 20 61 6e 64 20 60 6e 73 61 6d 70 6c 65 60 20 28 6e 75 6d 62 65 selection),.and.`nsample`.(numbe
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72fe0 73 0a 20 20 20 20 20 20 20 20 74 68 61 6e 20 6f 72 20 65 71 75 61 6c 20 74 6f 20 74 68 65 20 73 s.........than.or.equal.to.the.s
73000 75 6d 20 60 60 6e 67 6f 6f 64 20 2b 20 6e 62 61 64 60 60 29 2e 0a 0a 20 20 20 20 20 20 20 20 50 um.``ngood.+.nbad``)...........P
73020 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 arameters.........----------....
73040 20 20 20 20 20 6e 67 6f 6f 64 20 3a 20 69 6e 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f .....ngood.:.int.or.array_like.o
73060 66 20 69 6e 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 4e 75 6d 62 65 72 20 6f 66 20 77 61 79 f.ints.............Number.of.way
73080 73 20 74 6f 20 6d 61 6b 65 20 61 20 67 6f 6f 64 20 73 65 6c 65 63 74 69 6f 6e 2e 20 20 4d 75 73 s.to.make.a.good.selection...Mus
730a0 74 20 62 65 20 6e 6f 6e 6e 65 67 61 74 69 76 65 20 61 6e 64 0a 20 20 20 20 20 20 20 20 20 20 20 t.be.nonnegative.and............
730c0 20 6c 65 73 73 20 74 68 61 6e 20 31 30 2a 2a 39 2e 0a 20 20 20 20 20 20 20 20 6e 62 61 64 20 3a .less.than.10**9..........nbad.:
730e0 20 69 6e 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 69 6e 74 73 0a 20 20 20 20 20 .int.or.array_like.of.ints......
73100 20 20 20 20 20 20 20 4e 75 6d 62 65 72 20 6f 66 20 77 61 79 73 20 74 6f 20 6d 61 6b 65 20 61 20 .......Number.of.ways.to.make.a.
73120 62 61 64 20 73 65 6c 65 63 74 69 6f 6e 2e 20 20 4d 75 73 74 20 62 65 20 6e 6f 6e 6e 65 67 61 74 bad.selection...Must.be.nonnegat
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73160 2a 2a 39 2e 0a 20 20 20 20 20 20 20 20 6e 73 61 6d 70 6c 65 20 3a 20 69 6e 74 20 6f 72 20 61 72 **9..........nsample.:.int.or.ar
73180 72 61 79 5f 6c 69 6b 65 20 6f 66 20 69 6e 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 4e 75 6d ray_like.of.ints.............Num
731a0 62 65 72 20 6f 66 20 69 74 65 6d 73 20 73 61 6d 70 6c 65 64 2e 20 20 4d 75 73 74 20 62 65 20 6e ber.of.items.sampled...Must.be.n
731c0 6f 6e 6e 65 67 61 74 69 76 65 20 61 6e 64 20 6c 65 73 73 20 74 68 61 6e 0a 20 20 20 20 20 20 20 onnegative.and.less.than........
731e0 20 20 20 20 20 60 60 6e 67 6f 6f 64 20 2b 20 6e 62 61 64 60 60 2e 0a 20 20 20 20 20 20 20 20 73 .....``ngood.+.nbad``..........s
73200 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 ize.:.int.or.tuple.of.ints,.opti
73220 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 onal.............Output.shape...
73240 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 If.the.given.shape.is,.e.g.,.``(
73260 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d m,.n,.k)``,.then.............``m
73280 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 .*.n.*.k``.samples.are.drawn...I
732a0 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 f.size.is.``None``.(default),...
732c0 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 ..........a.single.value.is.retu
732e0 72 6e 65 64 20 69 66 20 60 6e 67 6f 6f 64 60 2c 20 60 6e 62 61 64 60 2c 20 61 6e 64 20 60 6e 73 rned.if.`ngood`,.`nbad`,.and.`ns
73300 61 6d 70 6c 65 60 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 72 65 20 61 6c 6c 20 73 63 61 6c 61 ample`.............are.all.scala
73320 72 73 2e 20 20 4f 74 68 65 72 77 69 73 65 2c 20 60 60 6e 70 2e 62 72 6f 61 64 63 61 73 74 28 6e rs...Otherwise,.``np.broadcast(n
73340 67 6f 6f 64 2c 20 6e 62 61 64 2c 20 6e 73 61 6d 70 6c 65 29 2e 73 69 7a 65 60 60 0a 20 20 20 20 good,.nbad,.nsample).size``.....
73360 20 20 20 20 20 20 20 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 ........samples.are.drawn.......
73380 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 ....Returns.........-------.....
733a0 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 ....out.:.ndarray.or.scalar.....
733c0 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 ........Drawn.samples.from.the.p
733e0 61 72 61 6d 65 74 65 72 69 7a 65 64 20 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 20 64 69 73 74 arameterized.hypergeometric.dist
73400 72 69 62 75 74 69 6f 6e 2e 20 45 61 63 68 0a 20 20 20 20 20 20 20 20 20 20 20 20 73 61 6d 70 6c ribution..Each.............sampl
73420 65 20 69 73 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 67 6f 6f 64 20 69 74 65 6d 73 20 77 69 e.is.the.number.of.good.items.wi
73440 74 68 69 6e 20 61 20 72 61 6e 64 6f 6d 6c 79 20 73 65 6c 65 63 74 65 64 20 73 75 62 73 65 74 20 thin.a.randomly.selected.subset.
73460 6f 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 73 69 7a 65 20 60 6e 73 61 6d 70 6c 65 60 20 74 61 of.............size.`nsample`.ta
73480 6b 65 6e 20 66 72 6f 6d 20 61 20 73 65 74 20 6f 66 20 60 6e 67 6f 6f 64 60 20 67 6f 6f 64 20 69 ken.from.a.set.of.`ngood`.good.i
734a0 74 65 6d 73 20 61 6e 64 20 60 6e 62 61 64 60 20 62 61 64 20 69 74 65 6d 73 2e 0a 0a 20 20 20 20 tems.and.`nbad`.bad.items.......
734c0 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 ....See.Also.........--------...
734e0 20 20 20 20 20 20 6d 75 6c 74 69 76 61 72 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 72 69 ......multivariate_hypergeometri
73500 63 20 3a 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 6d 75 6c 74 69 76 c.:.Draw.samples.from.the.multiv
73520 61 72 69 61 74 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 68 79 70 65 72 67 65 6f 6d 65 74 72 69 ariate.............hypergeometri
73540 63 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 c.distribution..........scipy.st
73560 61 74 73 2e 68 79 70 65 72 67 65 6f 6d 20 3a 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 ats.hypergeom.:.probability.dens
73580 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 6f 72 0a 20 20 ity.function,.distribution.or...
735a0 20 20 20 20 20 20 20 20 20 20 63 75 6d 75 6c 61 74 69 76 65 20 64 65 6e 73 69 74 79 20 66 75 6e ..........cumulative.density.fun
735c0 63 74 69 6f 6e 2c 20 65 74 63 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 ction,.etc...........Notes......
735e0 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 ...-----.........The.probability
73600 20 64 65 6e 73 69 74 79 20 66 6f 72 20 74 68 65 20 48 79 70 65 72 67 65 6f 6d 65 74 72 69 63 20 .density.for.the.Hypergeometric.
73620 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 distribution.is.............math
73640 3a 3a 20 50 28 78 29 20 3d 20 5c 66 72 61 63 7b 5c 62 69 6e 6f 6d 7b 67 7d 7b 78 7d 5c 62 69 6e ::.P(x).=.\frac{\binom{g}{x}\bin
73660 6f 6d 7b 62 7d 7b 6e 2d 78 7d 7d 7b 5c 62 69 6e 6f 6d 7b 67 2b 62 7d 7b 6e 7d 7d 2c 0a 0a 20 20 om{b}{n-x}}{\binom{g+b}{n}},....
73680 20 20 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 30 20 5c 6c 65 20 78 20 5c 6c 65 20 6e ......where.:math:`0.\le.x.\le.n
736a0 60 20 61 6e 64 20 3a 6d 61 74 68 3a 60 6e 2d 62 20 5c 6c 65 20 78 20 5c 6c 65 20 67 60 0a 0a 20 `.and.:math:`n-b.\le.x.\le.g`...
736c0 20 20 20 20 20 20 20 66 6f 72 20 50 28 78 29 20 74 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 .......for.P(x).the.probability.
736e0 6f 66 20 60 60 78 60 60 20 67 6f 6f 64 20 72 65 73 75 6c 74 73 20 69 6e 20 74 68 65 20 64 72 61 of.``x``.good.results.in.the.dra
73700 77 6e 20 73 61 6d 70 6c 65 2c 0a 20 20 20 20 20 20 20 20 67 20 3d 20 60 6e 67 6f 6f 64 60 2c 20 wn.sample,.........g.=.`ngood`,.
73720 62 20 3d 20 60 6e 62 61 64 60 2c 20 61 6e 64 20 6e 20 3d 20 60 6e 73 61 6d 70 6c 65 60 2e 0a 0a b.=.`nbad`,.and.n.=.`nsample`...
73740 20 20 20 20 20 20 20 20 43 6f 6e 73 69 64 65 72 20 61 6e 20 75 72 6e 20 77 69 74 68 20 62 6c 61 ........Consider.an.urn.with.bla
73760 63 6b 20 61 6e 64 20 77 68 69 74 65 20 6d 61 72 62 6c 65 73 20 69 6e 20 69 74 2c 20 60 6e 67 6f ck.and.white.marbles.in.it,.`ngo
73780 6f 64 60 20 6f 66 20 74 68 65 6d 0a 20 20 20 20 20 20 20 20 61 72 65 20 62 6c 61 63 6b 20 61 6e od`.of.them.........are.black.an
737a0 64 20 60 6e 62 61 64 60 20 61 72 65 20 77 68 69 74 65 2e 20 49 66 20 79 6f 75 20 64 72 61 77 20 d.`nbad`.are.white..If.you.draw.
737c0 60 6e 73 61 6d 70 6c 65 60 20 62 61 6c 6c 73 20 77 69 74 68 6f 75 74 0a 20 20 20 20 20 20 20 20 `nsample`.balls.without.........
737e0 72 65 70 6c 61 63 65 6d 65 6e 74 2c 20 74 68 65 6e 20 74 68 65 20 68 79 70 65 72 67 65 6f 6d 65 replacement,.then.the.hypergeome
73800 74 72 69 63 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 64 65 73 63 72 69 62 65 73 20 74 68 65 0a tric.distribution.describes.the.
73820 20 20 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 6f 66 20 62 6c 61 63 6b 20 62 61 ........distribution.of.black.ba
73840 6c 6c 73 20 69 6e 20 74 68 65 20 64 72 61 77 6e 20 73 61 6d 70 6c 65 2e 0a 0a 20 20 20 20 20 20 lls.in.the.drawn.sample.........
73860 20 20 4e 6f 74 65 20 74 68 61 74 20 74 68 69 73 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 ..Note.that.this.distribution.is
73880 20 76 65 72 79 20 73 69 6d 69 6c 61 72 20 74 6f 20 74 68 65 20 62 69 6e 6f 6d 69 61 6c 0a 20 20 .very.similar.to.the.binomial...
738a0 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 20 65 78 63 65 70 74 20 74 68 61 74 20 ......distribution,.except.that.
738c0 69 6e 20 74 68 69 73 20 63 61 73 65 2c 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 20 in.this.case,.samples.are.drawn.
738e0 77 69 74 68 6f 75 74 0a 20 20 20 20 20 20 20 20 72 65 70 6c 61 63 65 6d 65 6e 74 2c 20 77 68 65 without.........replacement,.whe
73900 72 65 61 73 20 69 6e 20 74 68 65 20 42 69 6e 6f 6d 69 61 6c 20 63 61 73 65 20 73 61 6d 70 6c 65 reas.in.the.Binomial.case.sample
73920 73 20 61 72 65 20 64 72 61 77 6e 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 72 65 70 6c 61 63 65 s.are.drawn.with.........replace
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73ac0 46 6f 72 20 73 75 63 68 20 6c 61 72 67 65 20 76 61 6c 75 65 73 2c 20 69 66 20 60 6e 73 61 6d 70 For.such.large.values,.if.`nsamp
73ae0 6c 65 60 20 69 73 20 6e 6f 74 20 61 6c 73 6f 20 6c 61 72 67 65 2c 0a 20 20 20 20 20 20 20 20 74 le`.is.not.also.large,.........t
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73b80 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d ....References.........---------
73ba0 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 4c 65 6e 74 6e 65 72 2c 20 4d 61 72 76 69 6e -............[1].Lentner,.Marvin
73bc0 2c 20 22 45 6c 65 6d 65 6e 74 61 72 79 20 41 70 70 6c 69 65 64 20 53 74 61 74 69 73 74 69 63 73 ,."Elementary.Applied.Statistics
73be0 22 2c 20 42 6f 67 64 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 61 6e 64 20 51 75 69 ",.Bogden................and.Qui
73c00 67 6c 65 79 2c 20 31 39 37 32 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 65 69 73 73 gley,.1972.............[2].Weiss
73c20 74 65 69 6e 2c 20 45 72 69 63 20 57 2e 20 22 48 79 70 65 72 67 65 6f 6d 65 74 72 69 63 20 44 69 tein,.Eric.W.."Hypergeometric.Di
73c40 73 74 72 69 62 75 74 69 6f 6e 2e 22 20 46 72 6f 6d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 stribution.".From...............
73c60 20 4d 61 74 68 57 6f 72 6c 64 2d 2d 41 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 65 73 6f 75 72 .MathWorld--A.Wolfram.Web.Resour
73c80 63 65 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d 61 74 68 77 6f ce.................http://mathwo
73ca0 72 6c 64 2e 77 6f 6c 66 72 61 6d 2e 63 6f 6d 2f 48 79 70 65 72 67 65 6f 6d 65 74 72 69 63 44 69 rld.wolfram.com/HypergeometricDi
73cc0 73 74 72 69 62 75 74 69 6f 6e 2e 68 74 6d 6c 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 33 5d 20 57 stribution.html............[3].W
73ce0 69 6b 69 70 65 64 69 61 2c 20 22 48 79 70 65 72 67 65 6f 6d 65 74 72 69 63 20 64 69 73 74 72 69 ikipedia,."Hypergeometric.distri
73d00 62 75 74 69 6f 6e 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f bution",................https://
73d20 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 48 79 70 65 72 67 65 6f 6d 65 en.wikipedia.org/wiki/Hypergeome
73d40 74 72 69 63 5f 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 34 5d tric_distribution............[4]
73d60 20 53 74 61 64 6c 6f 62 65 72 2c 20 45 72 6e 73 74 2c 20 22 54 68 65 20 72 61 74 69 6f 20 6f 66 .Stadlober,.Ernst,."The.ratio.of
73d80 20 75 6e 69 66 6f 72 6d 73 20 61 70 70 72 6f 61 63 68 20 66 6f 72 20 67 65 6e 65 72 61 74 69 6e .uniforms.approach.for.generatin
73da0 67 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 64 69 73 63 72 65 74 65 20 72 61 6e 64 6f 6d g................discrete.random
73dc0 20 76 61 72 69 61 74 65 73 22 2c 20 4a 6f 75 72 6e 61 6c 20 6f 66 20 43 6f 6d 70 75 74 61 74 69 .variates",.Journal.of.Computati
73de0 6f 6e 61 6c 20 61 6e 64 20 41 70 70 6c 69 65 64 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 onal.and.Applied................
73e00 4d 61 74 68 65 6d 61 74 69 63 73 2c 20 33 31 2c 20 70 70 2e 20 31 38 31 2d 31 38 39 20 28 31 39 Mathematics,.31,.pp..181-189.(19
73e20 39 30 29 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 90)...........Examples.........-
73e40 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f -------.........Draw.samples.fro
73e60 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e m.the.distribution:..........>>>
73e80 20 72 6e 67 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 .rng.=.np.random.default_rng()..
73ea0 20 20 20 20 20 20 20 3e 3e 3e 20 6e 67 6f 6f 64 2c 20 6e 62 61 64 2c 20 6e 73 61 6d 70 20 3d 20 .......>>>.ngood,.nbad,.nsamp.=.
73ec0 31 30 30 2c 20 32 2c 20 31 30 0a 20 20 20 20 20 20 20 20 23 20 6e 75 6d 62 65 72 20 6f 66 20 67 100,.2,.10.........#.number.of.g
73ee0 6f 6f 64 2c 20 6e 75 6d 62 65 72 20 6f 66 20 62 61 64 2c 20 61 6e 64 20 6e 75 6d 62 65 72 20 6f ood,.number.of.bad,.and.number.o
73f00 66 20 73 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 72 6e 67 2e 68 79 f.samples.........>>>.s.=.rng.hy
73f20 70 65 72 67 65 6f 6d 65 74 72 69 63 28 6e 67 6f 6f 64 2c 20 6e 62 61 64 2c 20 6e 73 61 6d 70 2c pergeometric(ngood,.nbad,.nsamp,
73f40 20 31 30 30 30 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6d 61 74 70 6c 6f 74 6c .1000).........>>>.from.matplotl
73f60 69 62 2e 70 79 70 6c 6f 74 20 69 6d 70 6f 72 74 20 68 69 73 74 0a 20 20 20 20 20 20 20 20 3e 3e ib.pyplot.import.hist.........>>
73f80 3e 20 68 69 73 74 28 73 29 0a 20 20 20 20 20 20 20 20 23 20 20 20 6e 6f 74 65 20 74 68 61 74 20 >.hist(s).........#...note.that.
73fa0 69 74 20 69 73 20 76 65 72 79 20 75 6e 6c 69 6b 65 6c 79 20 74 6f 20 67 72 61 62 20 62 6f 74 68 it.is.very.unlikely.to.grab.both
73fc0 20 62 61 64 20 69 74 65 6d 73 0a 0a 20 20 20 20 20 20 20 20 53 75 70 70 6f 73 65 20 79 6f 75 20 .bad.items..........Suppose.you.
73fe0 68 61 76 65 20 61 6e 20 75 72 6e 20 77 69 74 68 20 31 35 20 77 68 69 74 65 20 61 6e 64 20 31 35 have.an.urn.with.15.white.and.15
74000 20 62 6c 61 63 6b 20 6d 61 72 62 6c 65 73 2e 0a 20 20 20 20 20 20 20 20 49 66 20 79 6f 75 20 70 .black.marbles..........If.you.p
74020 75 6c 6c 20 31 35 20 6d 61 72 62 6c 65 73 20 61 74 20 72 61 6e 64 6f 6d 2c 20 68 6f 77 20 6c 69 ull.15.marbles.at.random,.how.li
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740c0 6d 28 73 3e 3d 31 32 29 2f 31 30 30 30 30 30 2e 20 2b 20 73 75 6d 28 73 3c 3d 33 29 2f 31 30 30 m(s>=12)/100000..+.sum(s<=3)/100
740e0 30 30 30 2e 0a 20 20 20 20 20 20 20 20 23 20 20 20 61 6e 73 77 65 72 20 3d 20 30 2e 30 30 33 20 000..........#...answer.=.0.003.
74100 2e 2e 2e 20 70 72 65 74 74 79 20 75 6e 6c 69 6b 65 6c 79 21 0a 0a 20 20 20 20 20 20 20 20 00 00 ....pretty.unlikely!............
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753a0 0d 68 03 00 04 82 00 00 01 28 0a 00 28 a8 02 00 1e 98 03 00 14 88 04 00 0b 78 05 00 06 d2 02 70 .h.......(..(............x.....p
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75440 1e 98 03 00 14 88 04 00 0b 78 05 00 06 d2 02 70 21 05 02 00 05 68 06 00 70 7c 00 00 ba 7c 00 00 .........x.....p!....h..p|...|..
75460 38 62 07 00 21 08 02 00 08 34 10 00 ba 7c 00 00 e5 7c 00 00 50 62 07 00 21 00 00 00 ba 7c 00 00 8b..!....4...|...|..Pb..!....|..
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754a0 09 68 03 00 04 82 00 00 01 15 05 00 15 78 02 00 0d 68 03 00 04 82 00 00 01 15 05 00 15 78 02 00 .h...........x...h...........x..
754c0 0d 68 03 00 04 82 00 00 01 28 0a 00 28 a8 02 00 1e 98 03 00 14 88 04 00 0b 78 05 00 06 d2 02 70 .h.......(..(............x.....p
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75520 dc 7f 00 00 c8 62 07 00 01 11 05 00 11 78 02 00 09 68 03 00 04 82 00 00 01 04 01 00 04 42 00 00 .....b.......x...h...........B..
75540 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 .....B.......B.......B.......B..
75560 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 .....B.......B.......B.......B..
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755a0 90 85 00 00 ff 85 00 00 d2 eb 04 00 00 00 00 00 51 86 00 00 5c 86 00 00 d2 eb 04 00 00 00 00 00 ................Q...\...........
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755e0 a4 86 00 00 c2 86 00 00 e9 eb 04 00 00 00 00 00 e2 86 00 00 ed 86 00 00 e9 eb 04 00 00 00 00 00 ................................
75600 01 04 01 00 04 42 00 00 09 1a 06 00 1a 34 0f 00 1a 72 16 e0 14 70 13 60 26 92 00 00 01 00 00 00 .....B.......4...r...p.`&.......
75620 25 87 00 00 0d 88 00 00 05 ec 04 00 0d 88 00 00 01 06 02 00 06 52 02 50 01 0f 06 00 0f 64 07 00 %....................R.P.....d..
75640 0f 34 06 00 0f 32 0b 70 01 09 01 00 09 62 00 00 01 08 04 00 08 72 04 70 03 60 02 30 01 06 02 00 .4...2.p.....b.......r.p.`.0....
75660 06 32 02 30 01 0d 04 00 0d 34 09 00 0d 32 06 50 09 04 01 00 04 22 00 00 26 92 00 00 01 00 00 00 .2.0.....4...2.P....."..&.......
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75740 06 52 02 30 01 06 02 00 06 32 02 30 01 18 0a 00 18 64 0c 00 18 54 0b 00 18 34 0a 00 18 52 14 f0 .R.0.....2.0.....d...T...4...R..
75760 12 e0 10 70 01 18 0a 00 18 64 0c 00 18 54 0b 00 18 34 0a 00 18 52 14 f0 12 e0 10 70 19 1b 03 00 ...p.....d...T...4...R.....p....
75780 09 01 24 00 02 30 00 00 2c eb 04 00 10 01 00 00 01 04 01 00 04 42 00 00 21 05 02 00 05 34 06 00 ..$..0..,............B..!....4..
757a0 00 9b 00 00 59 9b 00 00 90 65 07 00 21 08 04 00 08 74 04 00 00 34 06 00 00 9b 00 00 59 9b 00 00 ....Y....e..!....t...4......Y...
757c0 90 65 07 00 21 00 00 00 00 9b 00 00 59 9b 00 00 90 65 07 00 01 04 01 00 04 42 00 00 01 04 01 00 .e..!.......Y....e.......B......
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75800 00 34 06 00 00 9c 00 00 59 9c 00 00 dc 65 07 00 21 00 00 00 00 9c 00 00 59 9c 00 00 dc 65 07 00 .4......Y....e..!.......Y....e..
75820 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 21 05 02 00 05 34 06 00 .....B.......B.......B..!....4..
75840 20 9d 00 00 a2 9d 00 00 30 66 07 00 21 08 04 00 08 74 04 00 00 34 06 00 20 9d 00 00 a2 9d 00 00 ........0f..!....t...4..........
75860 30 66 07 00 21 00 00 00 20 9d 00 00 a2 9d 00 00 30 66 07 00 01 04 01 00 04 42 00 00 01 04 01 00 0f..!...........0f.......B......
75880 04 42 00 00 01 04 01 00 04 42 00 00 21 05 02 00 05 34 06 00 60 9e 00 00 e0 9e 00 00 84 66 07 00 .B.......B..!....4..`........f..
758a0 21 08 04 00 08 74 04 00 00 34 06 00 60 9e 00 00 e0 9e 00 00 84 66 07 00 01 04 01 00 04 42 00 00 !....t...4..`........f.......B..
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75920 04 54 43 00 40 a0 00 00 55 a0 00 00 fc 66 07 00 21 00 02 00 00 e4 3a 00 40 a0 00 00 55 a0 00 00 .TC.@...U....f..!.....:.@...U...
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75960 00 c4 3c 00 00 74 3d 00 00 64 3e 00 00 54 43 00 40 a0 00 00 55 a0 00 00 fc 66 07 00 01 0f 04 00 ..<..t=..d>..TC.@...U....f......
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759a0 16 e0 00 00 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 01 04 01 00 04 42 00 00 01 1a 0a 00 .........B.......B.......B......
759c0 1a 74 09 00 1a 64 08 00 1a 54 07 00 1a 34 06 00 1a 32 16 e0 01 1d 0a 00 1d f4 0a 00 15 34 0c 00 .t...d...T...4...2...........4..
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75a00 21 05 02 00 05 54 06 00 f0 b0 00 00 38 b1 00 00 ec 67 07 00 21 00 00 00 f0 b0 00 00 38 b1 00 00 !....T......8....g..!.......8...
75a20 ec 67 07 00 21 00 02 00 00 54 06 00 f0 b0 00 00 38 b1 00 00 ec 67 07 00 01 08 03 00 08 62 04 f0 .g..!....T......8....g.......b..
75a40 02 30 00 00 21 98 0c 00 98 64 0b 00 24 e4 04 00 1f d4 05 00 0f c4 06 00 0a 74 0c 00 05 54 0a 00 .0..!....d..$............t...T..
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75c20 0c 01 25 00 05 70 04 60 03 50 02 30 2c eb 04 00 10 01 00 00 01 1c 0c 00 1c 64 0c 00 1c 54 0b 00 ..%..p.`.P.0,............d...T..
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783c0 0e 98 07 00 1d 98 07 00 00 00 01 00 02 00 03 00 04 00 05 00 06 00 07 00 08 00 09 00 0a 00 0b 00 ................................
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78a40 d0 98 07 00 00 00 00 00 00 00 00 00 a4 b2 07 00 00 f0 04 00 50 99 07 00 00 00 00 00 00 00 00 00 ....................P...........
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78aa0 c8 f0 04 00 b8 9b 07 00 00 00 00 00 00 00 00 00 6a b6 07 00 e8 f2 04 00 00 00 00 00 00 00 00 00 ................j...............
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78ae0 52 b1 07 00 00 00 00 00 6c b1 07 00 00 00 00 00 80 b1 07 00 00 00 00 00 9c b1 07 00 00 00 00 00 R.......l.......................
78b00 ba b1 07 00 00 00 00 00 ce b1 07 00 00 00 00 00 e2 b1 07 00 00 00 00 00 18 b2 07 00 00 00 00 00 ................................
78b20 2e b2 07 00 00 00 00 00 44 b2 07 00 00 00 00 00 5e b2 07 00 00 00 00 00 7a b2 07 00 00 00 00 00 ........D.......^.......z.......
78b40 90 b2 07 00 00 00 00 00 00 00 00 00 00 00 00 00 96 b6 07 00 00 00 00 00 b2 b2 07 00 00 00 00 00 ................................
78b60 ca b2 07 00 00 00 00 00 ea b2 07 00 00 00 00 00 8c b6 07 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
78b80 28 b3 07 00 00 00 00 00 20 b3 07 00 00 00 00 00 00 00 00 00 00 00 00 00 f4 b4 07 00 00 00 00 00 (...............................
78ba0 ec b4 07 00 00 00 00 00 e4 b4 07 00 00 00 00 00 dc b4 07 00 00 00 00 00 d2 b4 07 00 00 00 00 00 ................................
78bc0 ca b4 07 00 00 00 00 00 c2 b4 07 00 00 00 00 00 ba b4 07 00 00 00 00 00 b2 b4 07 00 00 00 00 00 ................................
78be0 aa b4 07 00 00 00 00 00 a2 b4 07 00 00 00 00 00 98 b4 07 00 00 00 00 00 90 b4 07 00 00 00 00 00 ................................
78c00 88 b4 07 00 00 00 00 00 7e b4 07 00 00 00 00 00 76 b4 07 00 00 00 00 00 6c b4 07 00 00 00 00 00 ........~.......v.......l.......
78c20 60 b4 07 00 00 00 00 00 58 b4 07 00 00 00 00 00 4e b4 07 00 00 00 00 00 44 b4 07 00 00 00 00 00 `.......X.......N.......D.......
78c40 3a b4 07 00 00 00 00 00 32 b4 07 00 00 00 00 00 2a b4 07 00 00 00 00 00 22 b4 07 00 00 00 00 00 :.......2.......*.......".......
78c60 1a b4 07 00 00 00 00 00 fc b4 07 00 00 00 00 00 0a b4 07 00 00 00 00 00 02 b4 07 00 00 00 00 00 ................................
78c80 fa b3 07 00 00 00 00 00 f2 b3 07 00 00 00 00 00 e6 b3 07 00 00 00 00 00 de b3 07 00 00 00 00 00 ................................
78ca0 d6 b3 07 00 00 00 00 00 ce b3 07 00 00 00 00 00 c6 b3 07 00 00 00 00 00 ba b3 07 00 00 00 00 00 ................................
78cc0 b0 b3 07 00 00 00 00 00 a4 b3 07 00 00 00 00 00 9c b3 07 00 00 00 00 00 94 b3 07 00 00 00 00 00 ................................
78ce0 8c b3 07 00 00 00 00 00 86 b3 07 00 00 00 00 00 7e b3 07 00 00 00 00 00 78 b3 07 00 00 00 00 00 ................~.......x.......
78d00 70 b3 07 00 00 00 00 00 68 b3 07 00 00 00 00 00 60 b3 07 00 00 00 00 00 5a b3 07 00 00 00 00 00 p.......h.......`.......Z.......
78d20 54 b3 07 00 00 00 00 00 4c b3 07 00 00 00 00 00 44 b3 07 00 00 00 00 00 3c b3 07 00 00 00 00 00 T.......L.......D.......<.......
78d40 32 b3 07 00 00 00 00 00 04 b5 07 00 00 00 00 00 0e b5 07 00 00 00 00 00 1e b5 07 00 00 00 00 00 2...............................
78d60 28 b5 07 00 00 00 00 00 2e b5 07 00 00 00 00 00 36 b5 07 00 00 00 00 00 3e b5 07 00 00 00 00 00 (...............6.......>.......
78d80 46 b5 07 00 00 00 00 00 4c b5 07 00 00 00 00 00 54 b5 07 00 00 00 00 00 5c b5 07 00 00 00 00 00 F.......L.......T.......\.......
78da0 16 b5 07 00 00 00 00 00 12 b4 07 00 00 00 00 00 00 00 00 00 00 00 00 00 90 b5 07 00 00 00 00 00 ................................
78dc0 aa b5 07 00 00 00 00 00 cc b5 07 00 00 00 00 00 7e b5 07 00 00 00 00 00 00 b6 07 00 00 00 00 00 ................~...............
78de0 64 b5 07 00 00 00 00 00 e8 b5 07 00 00 00 00 00 70 b5 07 00 00 00 00 00 00 00 00 00 00 00 00 00 d...............p...............
78e00 06 b3 07 00 00 00 00 00 00 00 00 00 00 00 00 00 a0 aa 07 00 00 00 00 00 b4 aa 07 00 00 00 00 00 ................................
78e20 cc aa 07 00 00 00 00 00 e2 aa 07 00 00 00 00 00 fe aa 07 00 00 00 00 00 0c ab 07 00 00 00 00 00 ................................
78e40 1a ab 07 00 00 00 00 00 34 ab 07 00 00 00 00 00 4a ab 07 00 00 00 00 00 5a ab 07 00 00 00 00 00 ........4.......J.......Z.......
78e60 74 ab 07 00 00 00 00 00 82 ab 07 00 00 00 00 00 92 ab 07 00 00 00 00 00 a2 ab 07 00 00 00 00 00 t...............................
78e80 be ab 07 00 00 00 00 00 d2 ab 07 00 00 00 00 00 e0 ab 07 00 00 00 00 00 fc ab 07 00 00 00 00 00 ................................
78ea0 0c ac 07 00 00 00 00 00 30 ac 07 00 00 00 00 00 44 ac 07 00 00 00 00 00 56 ac 07 00 00 00 00 00 ........0.......D.......V.......
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78ee0 cc ac 07 00 00 00 00 00 e2 ac 07 00 00 00 00 00 f4 ac 07 00 00 00 00 00 02 ad 07 00 00 00 00 00 ................................
78f00 18 ad 07 00 00 00 00 00 28 ad 07 00 00 00 00 00 3c ad 07 00 00 00 00 00 4a ad 07 00 00 00 00 00 ........(.......<.......J.......
78f20 5c ad 07 00 00 00 00 00 74 ad 07 00 00 00 00 00 88 ad 07 00 00 00 00 00 9e ad 07 00 00 00 00 00 \.......t.......................
78f40 b2 ad 07 00 00 00 00 00 c2 ad 07 00 00 00 00 00 d6 ad 07 00 00 00 00 00 72 aa 07 00 00 00 00 00 ........................r.......
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78f80 5a ae 07 00 00 00 00 00 6a ae 07 00 00 00 00 00 7c ae 07 00 00 00 00 00 8e ae 07 00 00 00 00 00 Z.......j.......|...............
78fa0 a0 ae 07 00 00 00 00 00 b0 ae 07 00 00 00 00 00 90 aa 07 00 00 00 00 00 d6 ae 07 00 00 00 00 00 ................................
78fc0 e6 ae 07 00 00 00 00 00 f8 ae 07 00 00 00 00 00 0c af 07 00 00 00 00 00 24 af 07 00 00 00 00 00 ........................$.......
78fe0 38 af 07 00 00 00 00 00 4a af 07 00 00 00 00 00 62 af 07 00 00 00 00 00 76 af 07 00 00 00 00 00 8.......J.......b.......v.......
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79020 ec af 07 00 00 00 00 00 fa af 07 00 00 00 00 00 0c b0 07 00 00 00 00 00 22 b0 07 00 00 00 00 00 ........................".......
79040 38 b0 07 00 00 00 00 00 50 b0 07 00 00 00 00 00 64 b0 07 00 00 00 00 00 74 b0 07 00 00 00 00 00 8.......P.......d.......t.......
79060 86 b0 07 00 00 00 00 00 9a b0 07 00 00 00 00 00 aa b0 07 00 00 00 00 00 be b0 07 00 00 00 00 00 ................................
79080 ce b0 07 00 00 00 00 00 e2 b0 07 00 00 00 00 00 fa b0 07 00 00 00 00 00 18 b1 07 00 00 00 00 00 ................................
790a0 5a aa 07 00 00 00 00 00 42 aa 07 00 00 00 00 00 28 aa 07 00 00 00 00 00 18 aa 07 00 00 00 00 00 Z.......B.......(...............
790c0 06 aa 07 00 00 00 00 00 f2 a9 07 00 00 00 00 00 d8 a9 07 00 00 00 00 00 ca a9 07 00 00 00 00 00 ................................
790e0 b4 a9 07 00 00 00 00 00 a4 a9 07 00 00 00 00 00 90 a9 07 00 00 00 00 00 7c a9 07 00 00 00 00 00 ........................|.......
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79120 22 a9 07 00 00 00 00 00 10 a9 07 00 00 00 00 00 00 a9 07 00 00 00 00 00 f2 a8 07 00 00 00 00 00 "...............................
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79160 ae a8 07 00 00 00 00 00 9a a8 07 00 00 00 00 00 86 a8 07 00 00 00 00 00 72 a8 07 00 00 00 00 00 ........................r.......
79180 62 a8 07 00 00 00 00 00 4e a8 07 00 00 00 00 00 36 a8 07 00 00 00 00 00 1c a8 07 00 00 00 00 00 b.......N.......6...............
791a0 0a a8 07 00 00 00 00 00 f6 a7 07 00 00 00 00 00 e6 a7 07 00 00 00 00 00 ce a7 07 00 00 00 00 00 ................................
791c0 b8 a7 07 00 00 00 00 00 a8 a7 07 00 00 00 00 00 90 a7 07 00 00 00 00 00 7a a7 07 00 00 00 00 00 ........................z.......
791e0 6c a7 07 00 00 00 00 00 54 a7 07 00 00 00 00 00 3e a7 07 00 00 00 00 00 28 a7 07 00 00 00 00 00 l.......T.......>.......(.......
79200 14 a7 07 00 00 00 00 00 06 a7 07 00 00 00 00 00 f2 a6 07 00 00 00 00 00 e0 a6 07 00 00 00 00 00 ................................
79220 ca a6 07 00 00 00 00 00 b4 a6 07 00 00 00 00 00 98 a6 07 00 00 00 00 00 84 a6 07 00 00 00 00 00 ................................
79240 70 a6 07 00 00 00 00 00 5c a6 07 00 00 00 00 00 42 a6 07 00 00 00 00 00 32 a6 07 00 00 00 00 00 p.......\.......B.......2.......
79260 14 a6 07 00 00 00 00 00 f8 a5 07 00 00 00 00 00 de a5 07 00 00 00 00 00 ce a5 07 00 00 00 00 00 ................................
79280 b4 a5 07 00 00 00 00 00 a0 a5 07 00 00 00 00 00 90 a5 07 00 00 00 00 00 7a a5 07 00 00 00 00 00 ........................z.......
792a0 68 a5 07 00 00 00 00 00 50 a5 07 00 00 00 00 00 36 a5 07 00 00 00 00 00 20 a5 07 00 00 00 00 00 h.......P.......6...............
792c0 02 a5 07 00 00 00 00 00 ee a4 07 00 00 00 00 00 da a4 07 00 00 00 00 00 c6 a4 07 00 00 00 00 00 ................................
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7b400 37 60 60 2e 20 60 60 47 65 6e 65 72 61 74 6f 72 60 60 2c 20 62 65 73 69 64 65 73 20 62 65 69 6e 7``..``Generator``,.besides.bein
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7c2c0 49 74 20 6d 61 79 20 61 6c 73 6f 20 62 65 20 75 73 65 64 20 74 6f 20 6d 6f 64 65 6c 20 74 68 65 It.may.also.be.used.to.model.the
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7c340 2e 20 5b 31 5d 20 42 75 7a 61 73 2c 20 4d 61 72 74 69 6e 20 41 2e 3b 20 43 75 6c 76 65 72 2c 20 ..[1].Buzas,.Martin.A.;.Culver,.
7c360 53 74 65 70 68 65 6e 20 4a 2e 2c 20 20 55 6e 64 65 72 73 74 61 6e 64 69 6e 67 20 72 65 67 69 6f Stephen.J.,..Understanding.regio
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7c420 20 20 20 20 20 20 20 20 56 6f 6c 75 6d 65 20 35 2c 20 4e 75 6d 62 65 72 20 35 2c 20 53 65 70 74 ........Volume.5,.Number.5,.Sept
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7c4a0 54 68 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 72 65 6c 61 74 69 6f 6e 20 62 65 74 77 The................relation.betw
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7c940 61 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 69 73 20 67 65 6e 65 72 61 74 65 64 20 66 72 6f a.random.sample.is.generated.fro
7c960 6d 20 69 74 73 20 65 6c 65 6d 65 6e 74 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 61 m.its.elements..............If.a
7c980 6e 20 69 6e 74 2c 20 74 68 65 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 69 73 20 67 65 6e 65 n.int,.the.random.sample.is.gene
7c9a0 72 61 74 65 64 20 66 72 6f 6d 20 6e 70 2e 61 72 61 6e 67 65 28 61 29 2e 0a 20 20 20 20 20 20 20 rated.from.np.arange(a).........
7c9c0 20 73 69 7a 65 20 3a 20 7b 69 6e 74 2c 20 74 75 70 6c 65 5b 69 6e 74 5d 7d 2c 20 6f 70 74 69 6f .size.:.{int,.tuple[int]},.optio
7c9e0 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 nal.............Output.shape...I
7ca00 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d f.the.given.shape.is,.e.g.,.``(m
7ca20 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 ,.n,.k)``,.then.............``m.
7ca40 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 20 66 72 6f 6d *.n.*.k``.samples.are.drawn.from
7ca60 20 74 68 65 20 31 2d 64 20 60 61 60 2e 20 49 66 20 60 61 60 20 68 61 73 20 6d 6f 72 65 0a 20 20 .the.1-d.`a`..If.`a`.has.more...
7ca80 20 20 20 20 20 20 20 20 20 20 74 68 61 6e 20 6f 6e 65 20 64 69 6d 65 6e 73 69 6f 6e 2c 20 74 68 ..........than.one.dimension,.th
7caa0 65 20 60 73 69 7a 65 60 20 73 68 61 70 65 20 77 69 6c 6c 20 62 65 20 69 6e 73 65 72 74 65 64 20 e.`size`.shape.will.be.inserted.
7cac0 69 6e 74 6f 20 74 68 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 61 78 69 73 60 20 64 69 6d 65 into.the.............`axis`.dime
7cae0 6e 73 69 6f 6e 2c 20 73 6f 20 74 68 65 20 6f 75 74 70 75 74 20 60 60 6e 64 69 6d 60 60 20 77 69 nsion,.so.the.output.``ndim``.wi
7cb00 6c 6c 20 62 65 20 60 60 61 2e 6e 64 69 6d 20 2d 20 31 20 2b 0a 20 20 20 20 20 20 20 20 20 20 20 ll.be.``a.ndim.-.1.+............
7cb20 20 6c 65 6e 28 73 69 7a 65 29 60 60 2e 20 44 65 66 61 75 6c 74 20 69 73 20 4e 6f 6e 65 2c 20 69 .len(size)``..Default.is.None,.i
7cb40 6e 20 77 68 69 63 68 20 63 61 73 65 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 0a 20 n.which.case.a.single.value.is..
7cb60 20 20 20 20 20 20 20 20 20 20 20 72 65 74 75 72 6e 65 64 2e 0a 20 20 20 20 20 20 20 20 72 65 70 ...........returned..........rep
7cb80 6c 61 63 65 20 3a 20 62 6f 6f 6c 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 lace.:.bool,.optional...........
7cba0 20 20 57 68 65 74 68 65 72 20 74 68 65 20 73 61 6d 70 6c 65 20 69 73 20 77 69 74 68 20 6f 72 20 ..Whether.the.sample.is.with.or.
7cbc0 77 69 74 68 6f 75 74 20 72 65 70 6c 61 63 65 6d 65 6e 74 2e 20 44 65 66 61 75 6c 74 20 69 73 20 without.replacement..Default.is.
7cbe0 54 72 75 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 6d 65 61 6e 69 6e 67 20 74 68 61 74 20 61 True,.............meaning.that.a
7cc00 20 76 61 6c 75 65 20 6f 66 20 60 60 61 60 60 20 63 61 6e 20 62 65 20 73 65 6c 65 63 74 65 64 20 .value.of.``a``.can.be.selected.
7cc20 6d 75 6c 74 69 70 6c 65 20 74 69 6d 65 73 2e 0a 20 20 20 20 20 20 20 20 70 20 3a 20 31 2d 44 20 multiple.times..........p.:.1-D.
7cc40 61 72 72 61 79 5f 6c 69 6b 65 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 array_like,.optional............
7cc60 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 69 65 73 20 61 73 73 6f 63 69 61 74 65 64 20 77 69 .The.probabilities.associated.wi
7cc80 74 68 20 65 61 63 68 20 65 6e 74 72 79 20 69 6e 20 61 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 th.each.entry.in.a..............
7cca0 49 66 20 6e 6f 74 20 67 69 76 65 6e 2c 20 74 68 65 20 73 61 6d 70 6c 65 20 61 73 73 75 6d 65 73 If.not.given,.the.sample.assumes
7ccc0 20 61 20 75 6e 69 66 6f 72 6d 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 6f 76 65 72 20 61 6c 6c .a.uniform.distribution.over.all
7cce0 0a 20 20 20 20 20 20 20 20 20 20 20 20 65 6e 74 72 69 65 73 20 69 6e 20 60 60 61 60 60 2e 0a 20 .............entries.in.``a``...
7cd00 20 20 20 20 20 20 20 61 78 69 73 20 3a 20 69 6e 74 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 .......axis.:.int,.optional.....
7cd20 20 20 20 20 20 20 20 20 54 68 65 20 61 78 69 73 20 61 6c 6f 6e 67 20 77 68 69 63 68 20 74 68 65 ........The.axis.along.which.the
7cd40 20 73 65 6c 65 63 74 69 6f 6e 20 69 73 20 70 65 72 66 6f 72 6d 65 64 2e 20 54 68 65 20 64 65 66 .selection.is.performed..The.def
7cd60 61 75 6c 74 2c 20 30 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 73 65 6c 65 63 74 73 20 62 79 20 ault,.0,.............selects.by.
7cd80 72 6f 77 2e 0a 20 20 20 20 20 20 20 20 73 68 75 66 66 6c 65 20 3a 20 62 6f 6f 6c 2c 20 6f 70 74 row..........shuffle.:.bool,.opt
7cda0 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 57 68 65 74 68 65 72 20 74 68 65 20 73 61 ional.............Whether.the.sa
7cdc0 6d 70 6c 65 20 69 73 20 73 68 75 66 66 6c 65 64 20 77 68 65 6e 20 73 61 6d 70 6c 69 6e 67 20 77 mple.is.shuffled.when.sampling.w
7cde0 69 74 68 6f 75 74 20 72 65 70 6c 61 63 65 6d 65 6e 74 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 ithout.replacement..............
7ce00 44 65 66 61 75 6c 74 20 69 73 20 54 72 75 65 2c 20 46 61 6c 73 65 20 70 72 6f 76 69 64 65 73 20 Default.is.True,.False.provides.
7ce20 61 20 73 70 65 65 64 75 70 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 a.speedup...........Returns.....
7ce40 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 61 6d 70 6c 65 73 20 3a 20 73 69 ....-------.........samples.:.si
7ce60 6e 67 6c 65 20 69 74 65 6d 20 6f 72 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 20 20 20 ngle.item.or.ndarray............
7ce80 20 54 68 65 20 67 65 6e 65 72 61 74 65 64 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 73 0a 0a 20 .The.generated.random.samples...
7cea0 20 20 20 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 .......Raises.........------....
7cec0 20 20 20 20 20 56 61 6c 75 65 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 61 .....ValueError.............If.a
7cee0 20 69 73 20 61 6e 20 69 6e 74 20 61 6e 64 20 6c 65 73 73 20 74 68 61 6e 20 7a 65 72 6f 2c 20 69 .is.an.int.and.less.than.zero,.i
7cf00 66 20 70 20 69 73 20 6e 6f 74 20 31 2d 64 69 6d 65 6e 73 69 6f 6e 61 6c 2c 20 69 66 0a 20 20 20 f.p.is.not.1-dimensional,.if....
7cf20 20 20 20 20 20 20 20 20 20 61 20 69 73 20 61 72 72 61 79 2d 6c 69 6b 65 20 77 69 74 68 20 61 20 .........a.is.array-like.with.a.
7cf40 73 69 7a 65 20 30 2c 20 69 66 20 70 20 69 73 20 6e 6f 74 20 61 20 76 65 63 74 6f 72 20 6f 66 0a size.0,.if.p.is.not.a.vector.of.
7cf60 20 20 20 20 20 20 20 20 20 20 20 20 70 72 6f 62 61 62 69 6c 69 74 69 65 73 2c 20 69 66 20 61 20 ............probabilities,.if.a.
7cf80 61 6e 64 20 70 20 68 61 76 65 20 64 69 66 66 65 72 65 6e 74 20 6c 65 6e 67 74 68 73 2c 20 6f 72 and.p.have.different.lengths,.or
7cfa0 20 69 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 72 65 70 6c 61 63 65 3d 46 61 6c 73 65 20 61 6e .if.............replace=False.an
7cfc0 64 20 74 68 65 20 73 61 6d 70 6c 65 20 73 69 7a 65 20 69 73 20 67 72 65 61 74 65 72 20 74 68 61 d.the.sample.size.is.greater.tha
7cfe0 6e 20 74 68 65 20 70 6f 70 75 6c 61 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 73 69 7a n.the.population.............siz
7d000 65 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d e...........See.Also.........---
7d020 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 69 6e 74 65 67 65 72 73 2c 20 73 68 75 66 66 6c 65 2c -----.........integers,.shuffle,
7d040 20 70 65 72 6d 75 74 61 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 .permutation..........Notes.....
7d060 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 53 65 74 74 69 6e 67 20 75 73 65 72 2d 73 ....-----.........Setting.user-s
7d080 70 65 63 69 66 69 65 64 20 70 72 6f 62 61 62 69 6c 69 74 69 65 73 20 74 68 72 6f 75 67 68 20 60 pecified.probabilities.through.`
7d0a0 60 70 60 60 20 75 73 65 73 20 61 20 6d 6f 72 65 20 67 65 6e 65 72 61 6c 20 62 75 74 20 6c 65 73 `p``.uses.a.more.general.but.les
7d0c0 73 0a 20 20 20 20 20 20 20 20 65 66 66 69 63 69 65 6e 74 20 73 61 6d 70 6c 65 72 20 74 68 61 6e s.........efficient.sampler.than
7d0e0 20 74 68 65 20 64 65 66 61 75 6c 74 2e 20 54 68 65 20 67 65 6e 65 72 61 6c 20 73 61 6d 70 6c 65 .the.default..The.general.sample
7d100 72 20 70 72 6f 64 75 63 65 73 20 61 20 64 69 66 66 65 72 65 6e 74 20 73 61 6d 70 6c 65 0a 20 20 r.produces.a.different.sample...
7d120 20 20 20 20 20 20 74 68 61 6e 20 74 68 65 20 6f 70 74 69 6d 69 7a 65 64 20 73 61 6d 70 6c 65 72 ......than.the.optimized.sampler
7d140 20 65 76 65 6e 20 69 66 20 65 61 63 68 20 65 6c 65 6d 65 6e 74 20 6f 66 20 60 60 70 60 60 20 69 .even.if.each.element.of.``p``.i
7d160 73 20 31 20 2f 20 6c 65 6e 28 61 29 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a s.1./.len(a)...........Examples.
7d180 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 74 ........--------.........Generat
7d1a0 65 20 61 20 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 66 72 6f 6d 20 6e e.a.uniform.random.sample.from.n
7d1c0 70 2e 61 72 61 6e 67 65 28 35 29 20 6f 66 20 73 69 7a 65 20 33 3a 0a 0a 20 20 20 20 20 20 20 20 p.arange(5).of.size.3:..........
7d1e0 3e 3e 3e 20 72 6e 67 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 >>>.rng.=.np.random.default_rng(
7d200 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 35 2c 20 33 29 0a 20 ).........>>>.rng.choice(5,.3)..
7d220 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 30 2c 20 33 2c 20 34 5d 29 20 23 20 72 61 6e 64 6f 6d .......array([0,.3,.4]).#.random
7d240 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 23 54 68 69 73 20 69 73 20 65 71 75 69 76 61 6c 65 6e 74 .........>>>.#This.is.equivalent
7d260 20 74 6f 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 30 2c 35 2c 33 29 0a 0a 20 20 20 20 20 20 20 .to.rng.integers(0,5,3).........
7d280 20 47 65 6e 65 72 61 74 65 20 61 20 6e 6f 6e 2d 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 .Generate.a.non-uniform.random.s
7d2a0 61 6d 70 6c 65 20 66 72 6f 6d 20 6e 70 2e 61 72 61 6e 67 65 28 35 29 20 6f 66 20 73 69 7a 65 20 ample.from.np.arange(5).of.size.
7d2c0 33 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 35 2c 20 33 2c 3:..........>>>.rng.choice(5,.3,
7d2e0 20 70 3d 5b 30 2e 31 2c 20 30 2c 20 30 2e 33 2c 20 30 2e 36 2c 20 30 5d 29 0a 20 20 20 20 20 20 .p=[0.1,.0,.0.3,.0.6,.0]).......
7d300 20 20 61 72 72 61 79 28 5b 33 2c 20 33 2c 20 30 5d 29 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 ..array([3,.3,.0]).#.random.....
7d320 20 20 20 20 20 47 65 6e 65 72 61 74 65 20 61 20 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 .....Generate.a.uniform.random.s
7d340 61 6d 70 6c 65 20 66 72 6f 6d 20 6e 70 2e 61 72 61 6e 67 65 28 35 29 20 6f 66 20 73 69 7a 65 20 ample.from.np.arange(5).of.size.
7d360 33 20 77 69 74 68 6f 75 74 0a 20 20 20 20 20 20 20 20 72 65 70 6c 61 63 65 6d 65 6e 74 3a 0a 0a 3.without.........replacement:..
7d380 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 35 2c 20 33 2c 20 72 65 70 ........>>>.rng.choice(5,.3,.rep
7d3a0 6c 61 63 65 3d 46 61 6c 73 65 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 33 2c 31 2c 30 lace=False).........array([3,1,0
7d3c0 5d 29 20 23 20 72 61 6e 64 6f 6d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 23 54 68 69 73 20 69 73 ]).#.random.........>>>.#This.is
7d3e0 20 65 71 75 69 76 61 6c 65 6e 74 20 74 6f 20 72 6e 67 2e 70 65 72 6d 75 74 61 74 69 6f 6e 28 6e .equivalent.to.rng.permutation(n
7d400 70 2e 61 72 61 6e 67 65 28 35 29 29 5b 3a 33 5d 0a 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 p.arange(5))[:3]..........Genera
7d420 74 65 20 61 20 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 61 6d 70 6c 65 20 66 72 6f 6d 20 te.a.uniform.random.sample.from.
7d440 61 20 32 2d 44 20 61 72 72 61 79 20 61 6c 6f 6e 67 20 74 68 65 20 66 69 72 73 74 0a 20 20 20 20 a.2-D.array.along.the.first.....
7d460 20 20 20 20 61 78 69 73 20 28 74 68 65 20 64 65 66 61 75 6c 74 29 2c 20 77 69 74 68 6f 75 74 20 ....axis.(the.default),.without.
7d480 72 65 70 6c 61 63 65 6d 65 6e 74 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 replacement:..........>>>.rng.ch
7d4a0 6f 69 63 65 28 5b 5b 30 2c 20 31 2c 20 32 5d 2c 20 5b 33 2c 20 34 2c 20 35 5d 2c 20 5b 36 2c 20 oice([[0,.1,.2],.[3,.4,.5],.[6,.
7d4c0 37 2c 20 38 5d 5d 2c 20 32 2c 20 72 65 70 6c 61 63 65 3d 46 61 6c 73 65 29 0a 20 20 20 20 20 20 7,.8]],.2,.replace=False).......
7d4e0 20 20 61 72 72 61 79 28 5b 5b 33 2c 20 34 2c 20 35 5d 2c 20 23 20 72 61 6e 64 6f 6d 0a 20 20 20 ..array([[3,.4,.5],.#.random....
7d500 20 20 20 20 20 20 20 20 20 20 20 20 5b 30 2c 20 31 2c 20 32 5d 5d 29 0a 0a 20 20 20 20 20 20 20 ............[0,.1,.2]]).........
7d520 20 47 65 6e 65 72 61 74 65 20 61 20 6e 6f 6e 2d 75 6e 69 66 6f 72 6d 20 72 61 6e 64 6f 6d 20 73 .Generate.a.non-uniform.random.s
7d540 61 6d 70 6c 65 20 66 72 6f 6d 20 6e 70 2e 61 72 61 6e 67 65 28 35 29 20 6f 66 20 73 69 7a 65 0a ample.from.np.arange(5).of.size.
7d560 20 20 20 20 20 20 20 20 33 20 77 69 74 68 6f 75 74 20 72 65 70 6c 61 63 65 6d 65 6e 74 3a 0a 0a ........3.without.replacement:..
7d580 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 35 2c 20 33 2c 20 72 65 70 ........>>>.rng.choice(5,.3,.rep
7d5a0 6c 61 63 65 3d 46 61 6c 73 65 2c 20 70 3d 5b 30 2e 31 2c 20 30 2c 20 30 2e 33 2c 20 30 2e 36 2c lace=False,.p=[0.1,.0,.0.3,.0.6,
7d5c0 20 30 5d 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 32 2c 20 33 2c 20 30 5d 29 20 23 20 .0]).........array([2,.3,.0]).#.
7d5e0 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 41 6e 79 20 6f 66 20 74 68 65 20 61 62 6f 76 65 random..........Any.of.the.above
7d600 20 63 61 6e 20 62 65 20 72 65 70 65 61 74 65 64 20 77 69 74 68 20 61 6e 20 61 72 62 69 74 72 61 .can.be.repeated.with.an.arbitra
7d620 72 79 20 61 72 72 61 79 2d 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 69 6e 73 74 65 61 64 20 6f 66 ry.array-like.........instead.of
7d640 20 6a 75 73 74 20 69 6e 74 65 67 65 72 73 2e 20 46 6f 72 20 69 6e 73 74 61 6e 63 65 3a 0a 0a 20 .just.integers..For.instance:...
7d660 20 20 20 20 20 20 20 3e 3e 3e 20 61 61 5f 6d 69 6c 6e 65 5f 61 72 72 20 3d 20 5b 27 70 6f 6f 68 .......>>>.aa_milne_arr.=.['pooh
7d680 27 2c 20 27 72 61 62 62 69 74 27 2c 20 27 70 69 67 6c 65 74 27 2c 20 27 43 68 72 69 73 74 6f 70 ',.'rabbit',.'piglet',.'Christop
7d6a0 68 65 72 27 5d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 63 68 6f 69 63 65 28 61 61 5f her'].........>>>.rng.choice(aa_
7d6c0 6d 69 6c 6e 65 5f 61 72 72 2c 20 35 2c 20 70 3d 5b 30 2e 35 2c 20 30 2e 31 2c 20 30 2e 31 2c 20 milne_arr,.5,.p=[0.5,.0.1,.0.1,.
7d6e0 30 2e 33 5d 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 27 70 6f 6f 68 27 2c 20 27 70 6f 0.3]).........array(['pooh',.'po
7d700 6f 68 27 2c 20 27 70 6f 6f 68 27 2c 20 27 43 68 72 69 73 74 6f 70 68 65 72 27 2c 20 27 70 69 67 oh',.'pooh',.'Christopher',.'pig
7d720 6c 65 74 27 5d 2c 20 23 20 72 61 6e 64 6f 6d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 64 74 let'],.#.random...............dt
7d740 79 70 65 3d 27 3c 55 31 31 27 29 0a 0a 20 20 20 20 20 20 20 20 00 00 00 40 14 02 80 01 00 00 00 ype='<U11').............@.......
7d760 60 11 02 80 01 00 00 00 20 5b 01 80 01 00 00 00 0a 20 20 20 20 20 20 20 20 70 6f 77 65 72 28 61 `........[...............power(a
7d780 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 73 20 73 61 6d 70 ,.size=None)..........Draws.samp
7d7a0 6c 65 73 20 69 6e 20 5b 30 2c 20 31 5d 20 66 72 6f 6d 20 61 20 70 6f 77 65 72 20 64 69 73 74 72 les.in.[0,.1].from.a.power.distr
7d7c0 69 62 75 74 69 6f 6e 20 77 69 74 68 20 70 6f 73 69 74 69 76 65 0a 20 20 20 20 20 20 20 20 65 78 ibution.with.positive.........ex
7d7e0 70 6f 6e 65 6e 74 20 61 20 2d 20 31 2e 0a 0a 20 20 20 20 20 20 20 20 41 6c 73 6f 20 6b 6e 6f 77 ponent.a.-.1...........Also.know
7d800 6e 20 61 73 20 74 68 65 20 70 6f 77 65 72 20 66 75 6e 63 74 69 6f 6e 20 64 69 73 74 72 69 62 75 n.as.the.power.function.distribu
7d820 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 tion...........Parameters.......
7d840 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 61 20 3a 20 66 6c 6f 61 74 20 6f ..----------.........a.:.float.o
7d860 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 r.array_like.of.floats..........
7d880 20 20 20 50 61 72 61 6d 65 74 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e ...Parameter.of.the.distribution
7d8a0 2e 20 4d 75 73 74 20 62 65 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 2e 0a 20 20 20 20 20 20 20 20 ..Must.be.non-negative..........
7d8c0 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 size.:.int.or.tuple.of.ints,.opt
7d8e0 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 ional.............Output.shape..
7d900 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 .If.the.given.shape.is,.e.g.,.``
7d920 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 (m,.n,.k)``,.then.............``
7d940 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 m.*.n.*.k``.samples.are.drawn...
7d960 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 If.size.is.``None``.(default),..
7d980 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 ...........a.single.value.is.ret
7d9a0 75 72 6e 65 64 20 69 66 20 60 60 61 60 60 20 69 73 20 61 20 73 63 61 6c 61 72 2e 20 20 4f 74 68 urned.if.``a``.is.a.scalar...Oth
7d9c0 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6e 70 2e 61 72 72 61 79 28 61 erwise,.............``np.array(a
7d9e0 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 ).size``.samples.are.drawn......
7da00 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 .....Returns.........-------....
7da20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 .....out.:.ndarray.or.scalar....
7da40 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 .........Drawn.samples.from.the.
7da60 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 70 6f 77 65 72 20 64 69 73 74 72 69 62 75 74 69 6f 6e parameterized.power.distribution
7da80 2e 0a 0a 20 20 20 20 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d ...........Raises.........------
7daa0 0a 20 20 20 20 20 20 20 20 56 61 6c 75 65 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 .........ValueError.............
7dac0 49 66 20 61 20 3c 3d 20 30 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 If.a.<=.0...........Notes.......
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7ec80 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 28 60 73 74 61 6e 64 61 72 64 5f 6e 6f ......distribution.(`standard_no
7eca0 72 6d 61 6c 60 29 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 rmal`)...........Parameters.....
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7ece0 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 t.or.array_like.of.floats.......
7ed00 20 20 20 20 20 20 44 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 2c 20 6d 75 73 74 20 62 ......Degrees.of.freedom,.must.b
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7ed40 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 le.of.ints,.optional............
7ed60 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 .Output.shape...If.the.given.sha
7ed80 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e pe.is,.e.g.,.``(m,.n,.k)``,.then
7eda0 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c .............``m.*.n.*.k``.sampl
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7ee00 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 64 66 60 60 20 69 le.value.is.returned.if.``df``.i
7ee20 73 20 61 20 73 63 61 6c 61 72 2e 20 20 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 s.a.scalar...Otherwise,.........
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7ee60 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 s.are.drawn...........Returns...
7ee80 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 ......-------.........out.:.ndar
7eea0 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 ray.or.scalar.............Drawn.
7eec0 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 73 samples.from.the.parameterized.s
7eee0 74 61 6e 64 61 72 64 20 53 74 75 64 65 6e 74 27 73 20 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e tandard.Student's.t.distribution
7ef00 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 ...........Notes.........-----..
7ef20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 .......The.probability.density.f
7ef40 75 6e 63 74 69 6f 6e 20 66 6f 72 20 74 68 65 20 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 unction.for.the.t.distribution.i
7ef60 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 50 28 78 2c 20 64 66 29 20 3d 20 s.............math::.P(x,.df).=.
7ef80 5c 66 72 61 63 7b 5c 47 61 6d 6d 61 28 5c 66 72 61 63 7b 64 66 2b 31 7d 7b 32 7d 29 7d 7b 5c 73 \frac{\Gamma(\frac{df+1}{2})}{\s
7efa0 71 72 74 7b 5c 70 69 20 64 66 7d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5c 47 qrt{\pi.df}...................\G
7efc0 61 6d 6d 61 28 5c 66 72 61 63 7b 64 66 7d 7b 32 7d 29 7d 5c 42 69 67 6c 28 20 31 2b 5c 66 72 61 amma(\frac{df}{2})}\Bigl(.1+\fra
7efe0 63 7b 78 5e 32 7d 7b 64 66 7d 20 5c 42 69 67 72 29 5e 7b 2d 28 64 66 2b 31 29 2f 32 7d 0a 0a 20 c{x^2}{df}.\Bigr)^{-(df+1)/2}...
7f000 20 20 20 20 20 20 20 54 68 65 20 74 20 74 65 73 74 20 69 73 20 62 61 73 65 64 20 6f 6e 20 61 6e .......The.t.test.is.based.on.an
7f020 20 61 73 73 75 6d 70 74 69 6f 6e 20 74 68 61 74 20 74 68 65 20 64 61 74 61 20 63 6f 6d 65 20 66 .assumption.that.the.data.come.f
7f040 72 6f 6d 20 61 0a 20 20 20 20 20 20 20 20 4e 6f 72 6d 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f rom.a.........Normal.distributio
7f060 6e 2e 20 54 68 65 20 74 20 74 65 73 74 20 70 72 6f 76 69 64 65 73 20 61 20 77 61 79 20 74 6f 20 n..The.t.test.provides.a.way.to.
7f080 74 65 73 74 20 77 68 65 74 68 65 72 0a 20 20 20 20 20 20 20 20 74 68 65 20 73 61 6d 70 6c 65 20 test.whether.........the.sample.
7f0a0 6d 65 61 6e 20 28 74 68 61 74 20 69 73 20 74 68 65 20 6d 65 61 6e 20 63 61 6c 63 75 6c 61 74 65 mean.(that.is.the.mean.calculate
7f0c0 64 20 66 72 6f 6d 20 74 68 65 20 64 61 74 61 29 20 69 73 0a 20 20 20 20 20 20 20 20 61 20 67 6f d.from.the.data).is.........a.go
7f0e0 6f 64 20 65 73 74 69 6d 61 74 65 20 6f 66 20 74 68 65 20 74 72 75 65 20 6d 65 61 6e 2e 0a 0a 20 od.estimate.of.the.true.mean....
7f100 20 20 20 20 20 20 20 54 68 65 20 64 65 72 69 76 61 74 69 6f 6e 20 6f 66 20 74 68 65 20 74 2d 64 .......The.derivation.of.the.t-d
7f120 69 73 74 72 69 62 75 74 69 6f 6e 20 77 61 73 20 66 69 72 73 74 20 70 75 62 6c 69 73 68 65 64 20 istribution.was.first.published.
7f140 69 6e 0a 20 20 20 20 20 20 20 20 31 39 30 38 20 62 79 20 57 69 6c 6c 69 61 6d 20 47 6f 73 73 65 in.........1908.by.William.Gosse
7f160 74 20 77 68 69 6c 65 20 77 6f 72 6b 69 6e 67 20 66 6f 72 20 74 68 65 20 47 75 69 6e 6e 65 73 73 t.while.working.for.the.Guinness
7f180 20 42 72 65 77 65 72 79 0a 20 20 20 20 20 20 20 20 69 6e 20 44 75 62 6c 69 6e 2e 20 44 75 65 20 .Brewery.........in.Dublin..Due.
7f1a0 74 6f 20 70 72 6f 70 72 69 65 74 61 72 79 20 69 73 73 75 65 73 2c 20 68 65 20 68 61 64 20 74 6f to.proprietary.issues,.he.had.to
7f1c0 20 70 75 62 6c 69 73 68 20 75 6e 64 65 72 0a 20 20 20 20 20 20 20 20 61 20 70 73 65 75 64 6f 6e .publish.under.........a.pseudon
7f1e0 79 6d 2c 20 61 6e 64 20 73 6f 20 68 65 20 75 73 65 64 20 74 68 65 20 6e 61 6d 65 20 53 74 75 64 ym,.and.so.he.used.the.name.Stud
7f200 65 6e 74 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 ent...........References........
7f220 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 44 61 6c 67 61 .----------............[1].Dalga
7f240 61 72 64 2c 20 50 65 74 65 72 2c 20 22 49 6e 74 72 6f 64 75 63 74 6f 72 79 20 53 74 61 74 69 73 ard,.Peter,."Introductory.Statis
7f260 74 69 63 73 20 57 69 74 68 20 52 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 53 70 72 tics.With.R",................Spr
7f280 69 6e 67 65 72 2c 20 32 30 30 32 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 69 6b 69 inger,.2002.............[2].Wiki
7f2a0 70 65 64 69 61 2c 20 22 53 74 75 64 65 6e 74 27 73 20 74 2d 64 69 73 74 72 69 62 75 74 69 6f 6e pedia,."Student's.t-distribution
7f2c0 22 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 "................https://en.wiki
7f2e0 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 53 74 75 64 65 6e 74 27 73 5f 74 2d 64 69 73 74 72 pedia.org/wiki/Student's_t-distr
7f300 69 62 75 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 ibution..........Examples.......
7f320 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 46 72 6f 6d 20 44 61 6c 67 61 61 72 64 ..--------.........From.Dalgaard
7f340 20 70 61 67 65 20 38 33 20 5b 31 5d 5f 2c 20 73 75 70 70 6f 73 65 20 74 68 65 20 64 61 69 6c 79 .page.83.[1]_,.suppose.the.daily
7f360 20 65 6e 65 72 67 79 20 69 6e 74 61 6b 65 20 66 6f 72 20 31 31 0a 20 20 20 20 20 20 20 20 77 6f .energy.intake.for.11.........wo
7f380 6d 65 6e 20 69 6e 20 6b 69 6c 6f 6a 6f 75 6c 65 73 20 28 6b 4a 29 20 69 73 3a 0a 0a 20 20 20 20 men.in.kilojoules.(kJ).is:......
7f3a0 20 20 20 20 3e 3e 3e 20 69 6e 74 61 6b 65 20 3d 20 6e 70 2e 61 72 72 61 79 28 5b 35 32 36 30 2e ....>>>.intake.=.np.array([5260.
7f3c0 2c 20 35 34 37 30 2c 20 35 36 34 30 2c 20 36 31 38 30 2c 20 36 33 39 30 2c 20 36 35 31 35 2c 20 ,.5470,.5640,.6180,.6390,.6515,.
7f3e0 36 38 30 35 2c 20 37 35 31 35 2c 20 5c 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 20 20 6805,.7515,.\...................
7f400 20 20 20 20 20 20 20 20 20 20 20 20 20 37 35 31 35 2c 20 38 32 33 30 2c 20 38 37 37 30 5d 29 0a .............7515,.8230,.8770]).
7f420 0a 20 20 20 20 20 20 20 20 44 6f 65 73 20 74 68 65 69 72 20 65 6e 65 72 67 79 20 69 6e 74 61 6b .........Does.their.energy.intak
7f440 65 20 64 65 76 69 61 74 65 20 73 79 73 74 65 6d 61 74 69 63 61 6c 6c 79 20 66 72 6f 6d 20 74 68 e.deviate.systematically.from.th
7f460 65 20 72 65 63 6f 6d 6d 65 6e 64 65 64 0a 20 20 20 20 20 20 20 20 76 61 6c 75 65 20 6f 66 20 37 e.recommended.........value.of.7
7f480 37 32 35 20 6b 4a 3f 20 4f 75 72 20 6e 75 6c 6c 20 68 79 70 6f 74 68 65 73 69 73 20 77 69 6c 6c 725.kJ?.Our.null.hypothesis.will
7f4a0 20 62 65 20 74 68 65 20 61 62 73 65 6e 63 65 20 6f 66 20 64 65 76 69 61 74 69 6f 6e 2c 0a 20 20 .be.the.absence.of.deviation,...
7f4c0 20 20 20 20 20 20 61 6e 64 20 74 68 65 20 61 6c 74 65 72 6e 61 74 65 20 68 79 70 6f 74 68 65 73 ......and.the.alternate.hypothes
7f4e0 69 73 20 77 69 6c 6c 20 62 65 20 74 68 65 20 70 72 65 73 65 6e 63 65 20 6f 66 20 61 6e 20 65 66 is.will.be.the.presence.of.an.ef
7f500 66 65 63 74 20 74 68 61 74 20 63 6f 75 6c 64 20 62 65 0a 20 20 20 20 20 20 20 20 65 69 74 68 65 fect.that.could.be.........eithe
7f520 72 20 70 6f 73 69 74 69 76 65 20 6f 72 20 6e 65 67 61 74 69 76 65 2c 20 68 65 6e 63 65 20 6d 61 r.positive.or.negative,.hence.ma
7f540 6b 69 6e 67 20 6f 75 72 20 74 65 73 74 20 32 2d 74 61 69 6c 65 64 2e 20 0a 0a 20 20 20 20 20 20 king.our.test.2-tailed..........
7f560 20 20 42 65 63 61 75 73 65 20 77 65 20 61 72 65 20 65 73 74 69 6d 61 74 69 6e 67 20 74 68 65 20 ..Because.we.are.estimating.the.
7f580 6d 65 61 6e 20 61 6e 64 20 77 65 20 68 61 76 65 20 4e 3d 31 31 20 76 61 6c 75 65 73 20 69 6e 20 mean.and.we.have.N=11.values.in.
7f5a0 6f 75 72 20 73 61 6d 70 6c 65 2c 0a 20 20 20 20 20 20 20 20 77 65 20 68 61 76 65 20 4e 2d 31 3d our.sample,.........we.have.N-1=
7f5c0 31 30 20 64 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 2e 20 57 65 20 73 65 74 20 6f 75 10.degrees.of.freedom..We.set.ou
7f5e0 72 20 73 69 67 6e 69 66 69 63 61 6e 63 65 20 6c 65 76 65 6c 20 74 6f 20 39 35 25 20 61 6e 64 20 r.significance.level.to.95%.and.
7f600 0a 20 20 20 20 20 20 20 20 63 6f 6d 70 75 74 65 20 74 68 65 20 74 20 73 74 61 74 69 73 74 69 63 .........compute.the.t.statistic
7f620 20 75 73 69 6e 67 20 74 68 65 20 65 6d 70 69 72 69 63 61 6c 20 6d 65 61 6e 20 61 6e 64 20 65 6d .using.the.empirical.mean.and.em
7f640 70 69 72 69 63 61 6c 20 73 74 61 6e 64 61 72 64 20 0a 20 20 20 20 20 20 20 20 64 65 76 69 61 74 pirical.standard..........deviat
7f660 69 6f 6e 20 6f 66 20 6f 75 72 20 69 6e 74 61 6b 65 2e 20 57 65 20 75 73 65 20 61 20 64 64 6f 66 ion.of.our.intake..We.use.a.ddof
7f680 20 6f 66 20 31 20 74 6f 20 62 61 73 65 20 74 68 65 20 63 6f 6d 70 75 74 61 74 69 6f 6e 20 6f 66 .of.1.to.base.the.computation.of
7f6a0 20 6f 75 72 20 0a 20 20 20 20 20 20 20 20 65 6d 70 69 72 69 63 61 6c 20 73 74 61 6e 64 61 72 64 .our..........empirical.standard
7f6c0 20 64 65 76 69 61 74 69 6f 6e 20 6f 6e 20 61 6e 20 75 6e 62 69 61 73 65 64 20 65 73 74 69 6d 61 .deviation.on.an.unbiased.estima
7f6e0 74 65 20 6f 66 20 74 68 65 20 76 61 72 69 61 6e 63 65 20 28 6e 6f 74 65 3a 0a 20 20 20 20 20 20 te.of.the.variance.(note:.......
7f700 20 20 74 68 65 20 66 69 6e 61 6c 20 65 73 74 69 6d 61 74 65 20 69 73 20 6e 6f 74 20 75 6e 62 69 ..the.final.estimate.is.not.unbi
7f720 61 73 65 64 20 64 75 65 20 74 6f 20 74 68 65 20 63 6f 6e 63 61 76 65 20 6e 61 74 75 72 65 20 6f ased.due.to.the.concave.nature.o
7f740 66 20 74 68 65 20 73 71 75 61 72 65 20 0a 20 20 20 20 20 20 20 20 72 6f 6f 74 29 2e 0a 0a 20 20 f.the.square..........root).....
7f760 20 20 20 20 20 20 3e 3e 3e 20 6e 70 2e 6d 65 61 6e 28 69 6e 74 61 6b 65 29 0a 20 20 20 20 20 20 ......>>>.np.mean(intake).......
7f780 20 20 36 37 35 33 2e 36 33 36 33 36 33 36 33 36 33 36 34 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 ..6753.636363636364.........>>>.
7f7a0 69 6e 74 61 6b 65 2e 73 74 64 28 64 64 6f 66 3d 31 29 0a 20 20 20 20 20 20 20 20 31 31 34 32 2e intake.std(ddof=1).........1142.
7f7c0 31 32 33 32 32 32 31 33 37 33 37 32 37 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 74 20 3d 20 28 6e 1232221373727.........>>>.t.=.(n
7f7e0 70 2e 6d 65 61 6e 28 69 6e 74 61 6b 65 29 2d 37 37 32 35 29 2f 28 69 6e 74 61 6b 65 2e 73 74 64 p.mean(intake)-7725)/(intake.std
7f800 28 64 64 6f 66 3d 31 29 2f 6e 70 2e 73 71 72 74 28 6c 65 6e 28 69 6e 74 61 6b 65 29 29 29 0a 20 (ddof=1)/np.sqrt(len(intake)))..
7f820 20 20 20 20 20 20 20 3e 3e 3e 20 74 0a 20 20 20 20 20 20 20 20 2d 32 2e 38 32 30 37 35 34 30 36 .......>>>.t.........-2.82075406
7f840 30 38 33 31 30 31 39 38 0a 0a 20 20 20 20 20 20 20 20 57 65 20 64 72 61 77 20 31 30 30 30 30 30 08310198..........We.draw.100000
7f860 30 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 53 74 75 64 65 6e 74 27 73 20 74 20 64 69 73 74 72 0.samples.from.Student's.t.distr
7f880 69 62 75 74 69 6f 6e 20 77 69 74 68 20 74 68 65 20 61 64 65 71 75 61 74 65 0a 20 20 20 20 20 20 ibution.with.the.adequate.......
7f8a0 20 20 64 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 2e 0a 0a 20 20 20 20 20 20 20 20 3e ..degrees.of.freedom...........>
7f8c0 3e 3e 20 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 >>.import.matplotlib.pyplot.as.p
7f8e0 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 lt.........>>>.s.=.np.random.def
7f900 61 75 6c 74 5f 72 6e 67 28 29 2e 73 74 61 6e 64 61 72 64 5f 74 28 31 30 2c 20 73 69 7a 65 3d 31 ault_rng().standard_t(10,.size=1
7f920 30 30 30 30 30 30 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 68 20 3d 20 70 6c 74 2e 68 69 73 74 000000).........>>>.h.=.plt.hist
7f940 28 73 2c 20 62 69 6e 73 3d 31 30 30 2c 20 64 65 6e 73 69 74 79 3d 54 72 75 65 29 0a 0a 20 20 20 (s,.bins=100,.density=True).....
7f960 20 20 20 20 20 44 6f 65 73 20 6f 75 72 20 74 20 73 74 61 74 69 73 74 69 63 20 6c 61 6e 64 20 69 .....Does.our.t.statistic.land.i
7f980 6e 20 6f 6e 65 20 6f 66 20 74 68 65 20 74 77 6f 20 63 72 69 74 69 63 61 6c 20 72 65 67 69 6f 6e n.one.of.the.two.critical.region
7f9a0 73 20 66 6f 75 6e 64 20 61 74 20 0a 20 20 20 20 20 20 20 20 62 6f 74 68 20 74 61 69 6c 73 20 6f s.found.at..........both.tails.o
7f9c0 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 3f 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e f.the.distribution?..........>>>
7f9e0 20 6e 70 2e 73 75 6d 28 6e 70 2e 61 62 73 28 74 29 20 3c 20 6e 70 2e 61 62 73 28 73 29 29 20 2f .np.sum(np.abs(t).<.np.abs(s))./
7fa00 20 66 6c 6f 61 74 28 6c 65 6e 28 73 29 29 0a 20 20 20 20 20 20 20 20 30 2e 30 31 38 33 31 38 20 .float(len(s)).........0.018318.
7fa20 20 23 72 61 6e 64 6f 6d 20 3c 20 30 2e 30 35 2c 20 73 74 61 74 69 73 74 69 63 20 69 73 20 69 6e .#random.<.0.05,.statistic.is.in
7fa40 20 63 72 69 74 69 63 61 6c 20 72 65 67 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 .critical.region..........The.pr
7fa60 6f 62 61 62 69 6c 69 74 79 20 76 61 6c 75 65 20 66 6f 72 20 74 68 69 73 20 32 2d 74 61 69 6c 65 obability.value.for.this.2-taile
7fa80 64 20 74 65 73 74 20 69 73 20 61 62 6f 75 74 20 31 2e 38 33 25 2c 20 77 68 69 63 68 20 69 73 20 d.test.is.about.1.83%,.which.is.
7faa0 0a 20 20 20 20 20 20 20 20 6c 6f 77 65 72 20 74 68 61 6e 20 74 68 65 20 35 25 20 70 72 65 2d 64 .........lower.than.the.5%.pre-d
7fac0 65 74 65 72 6d 69 6e 65 64 20 73 69 67 6e 69 66 69 63 61 6e 63 65 20 74 68 72 65 73 68 6f 6c 64 etermined.significance.threshold
7fae0 2e 20 0a 0a 20 20 20 20 20 20 20 20 54 68 65 72 65 66 6f 72 65 2c 20 74 68 65 20 70 72 6f 62 61 ............Therefore,.the.proba
7fb00 62 69 6c 69 74 79 20 6f 66 20 6f 62 73 65 72 76 69 6e 67 20 76 61 6c 75 65 73 20 61 73 20 65 78 bility.of.observing.values.as.ex
7fb20 74 72 65 6d 65 20 61 73 20 6f 75 72 20 69 6e 74 61 6b 65 0a 20 20 20 20 20 20 20 20 63 6f 6e 64 treme.as.our.intake.........cond
7fb40 69 74 69 6f 6e 61 6c 6c 79 20 6f 6e 20 74 68 65 20 6e 75 6c 6c 20 68 79 70 6f 74 68 65 73 69 73 itionally.on.the.null.hypothesis
7fb60 20 62 65 69 6e 67 20 74 72 75 65 20 69 73 20 74 6f 6f 20 6c 6f 77 2c 20 61 6e 64 20 77 65 20 72 .being.true.is.too.low,.and.we.r
7fb80 65 6a 65 63 74 20 0a 20 20 20 20 20 20 20 20 74 68 65 20 6e 75 6c 6c 20 68 79 70 6f 74 68 65 73 eject..........the.null.hypothes
7fba0 69 73 20 6f 66 20 6e 6f 20 64 65 76 69 61 74 69 6f 6e 2e 20 0a 0a 20 20 20 20 20 20 20 20 00 00 is.of.no.deviation..............
7fbc0 e0 c3 07 80 01 00 00 00 b0 5f 01 80 01 00 00 00 00 00 00 00 00 00 00 00 f0 c3 07 80 01 00 00 00 ........._......................
7fbe0 00 00 00 00 00 00 00 00 c0 c4 07 80 01 00 00 00 90 5f 01 80 01 00 00 00 10 5f 01 80 01 00 00 00 ................._......._......
7fc00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
7fc20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
7fc40 0a 20 20 20 20 20 20 20 20 76 6f 6e 6d 69 73 65 73 28 6d 75 2c 20 6b 61 70 70 61 2c 20 73 69 7a .........vonmises(mu,.kappa,.siz
7fc60 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 e=None)..........Draw.samples.fr
7fc80 6f 6d 20 61 20 76 6f 6e 20 4d 69 73 65 73 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 om.a.von.Mises.distribution.....
7fca0 20 20 20 20 20 20 53 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 20 66 72 6f 6d 20 61 20 76 ......Samples.are.drawn.from.a.v
7fcc0 6f 6e 20 4d 69 73 65 73 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 77 69 74 68 20 73 70 65 63 69 on.Mises.distribution.with.speci
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7fd20 2d 70 69 2c 20 70 69 5d 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 76 6f 6e 20 4d 69 73 65 73 -pi,.pi]...........The.von.Mises
7fd40 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 28 61 6c 73 6f 20 6b 6e 6f 77 6e 20 61 73 20 74 68 65 .distribution.(also.known.as.the
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7fe20 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d ........Parameters.........-----
7fe40 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6d 75 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 -----.........mu.:.float.or.arra
7fe60 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 4d 6f 64 y_like.of.floats.............Mod
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7fea0 2e 0a 20 20 20 20 20 20 20 20 6b 61 70 70 61 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 ..........kappa.:.float.or.array
7fec0 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 69 73 70 _like.of.floats.............Disp
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7ff00 74 6f 20 62 65 20 3e 3d 30 2e 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 to.be.>=0..........size.:.int.or
7ff20 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 .tuple.of.ints,.optional........
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7ff80 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 then.............``m.*.n.*.k``.s
7ffa0 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 amples.are.drawn...If.size.is.``
7ffc0 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 None``.(default),.............a.
7ffe0 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 6d 75 single.value.is.returned.if.``mu
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80040 72 6f 61 64 63 61 73 74 28 6d 75 2c 20 6b 61 70 70 61 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c roadcast(mu,.kappa).size``.sampl
80060 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 es.are.drawn...........Returns..
80080 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 .......-------.........out.:.nda
800a0 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e rray.or.scalar.............Drawn
800c0 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 .samples.from.the.parameterized.
800e0 76 6f 6e 20 4d 69 73 65 73 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 von.Mises.distribution..........
80100 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 .See.Also.........--------......
80120 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 76 6f 6e 6d 69 73 65 73 20 3a 20 70 72 6f 62 61 62 ...scipy.stats.vonmises.:.probab
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80180 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 2c 20 65 74 63 2e 0a 0a 20 20 20 20 20 20 20 20 density.function,.etc...........
801a0 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 Notes.........-----.........The.
801c0 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 6f 72 20 74 68 65 20 76 6f 6e 20 probability.density.for.the.von.
801e0 4d 69 73 65 73 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e Mises.distribution.is...........
80200 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 5c 66 72 61 63 7b 65 5e 7b 5c 6b 61 70 70 61 20 ..math::.p(x).=.\frac{e^{\kappa.
80220 63 6f 73 28 78 2d 5c 6d 75 29 7d 7d 7b 32 5c 70 69 20 49 5f 30 28 5c 6b 61 70 70 61 29 7d 2c 0a cos(x-\mu)}}{2\pi.I_0(\kappa)},.
80240 0a 20 20 20 20 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 5c 6d 75 60 20 69 73 20 74 68 .........where.:math:`\mu`.is.th
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802c0 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 6f 72 64 65 72 20 30 2e 0a 0a 20 20 20 20 20 20 20 20 54 .function.of.order.0...........T
802e0 68 65 20 76 6f 6e 20 4d 69 73 65 73 20 69 73 20 6e 61 6d 65 64 20 66 6f 72 20 52 69 63 68 61 72 he.von.Mises.is.named.for.Richar
80300 64 20 45 64 6c 65 72 20 76 6f 6e 20 4d 69 73 65 73 2c 20 77 68 6f 20 77 61 73 20 62 6f 72 6e 20 d.Edler.von.Mises,.who.was.born.
80320 69 6e 0a 20 20 20 20 20 20 20 20 41 75 73 74 72 69 61 2d 48 75 6e 67 61 72 79 2c 20 69 6e 20 77 in.........Austria-Hungary,.in.w
80340 68 61 74 20 69 73 20 6e 6f 77 20 74 68 65 20 55 6b 72 61 69 6e 65 2e 20 20 48 65 20 66 6c 65 64 hat.is.now.the.Ukraine...He.fled
80360 20 74 6f 20 74 68 65 20 55 6e 69 74 65 64 0a 20 20 20 20 20 20 20 20 53 74 61 74 65 73 20 69 6e .to.the.United.........States.in
80380 20 31 39 33 39 20 61 6e 64 20 62 65 63 61 6d 65 20 61 20 70 72 6f 66 65 73 73 6f 72 20 61 74 20 .1939.and.became.a.professor.at.
803a0 48 61 72 76 61 72 64 2e 20 20 48 65 20 77 6f 72 6b 65 64 20 69 6e 0a 20 20 20 20 20 20 20 20 70 Harvard...He.worked.in.........p
803c0 72 6f 62 61 62 69 6c 69 74 79 20 74 68 65 6f 72 79 2c 20 61 65 72 6f 64 79 6e 61 6d 69 63 73 2c robability.theory,.aerodynamics,
803e0 20 66 6c 75 69 64 20 6d 65 63 68 61 6e 69 63 73 2c 20 61 6e 64 20 70 68 69 6c 6f 73 6f 70 68 79 .fluid.mechanics,.and.philosophy
80400 20 6f 66 0a 20 20 20 20 20 20 20 20 73 63 69 65 6e 63 65 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 .of.........science...........Re
80420 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 ferences.........----------.....
80440 20 20 20 20 2e 2e 20 5b 31 5d 20 41 62 72 61 6d 6f 77 69 74 7a 2c 20 4d 2e 20 61 6e 64 20 53 74 .......[1].Abramowitz,.M..and.St
80460 65 67 75 6e 2c 20 49 2e 20 41 2e 20 28 45 64 73 2e 29 2e 20 22 48 61 6e 64 62 6f 6f 6b 20 6f 66 egun,.I..A..(Eds.).."Handbook.of
80480 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 4d 61 74 68 65 6d 61 74 69 63 61 6c 20 46 75 6e ................Mathematical.Fun
804a0 63 74 69 6f 6e 73 20 77 69 74 68 20 46 6f 72 6d 75 6c 61 73 2c 20 47 72 61 70 68 73 2c 20 61 6e ctions.with.Formulas,.Graphs,.an
804c0 64 20 4d 61 74 68 65 6d 61 74 69 63 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 54 61 d.Mathematical................Ta
804e0 62 6c 65 73 2c 20 39 74 68 20 70 72 69 6e 74 69 6e 67 2c 22 20 4e 65 77 20 59 6f 72 6b 3a 20 44 bles,.9th.printing,".New.York:.D
80500 6f 76 65 72 2c 20 31 39 37 32 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 76 6f 6e 20 4d over,.1972.............[2].von.M
80520 69 73 65 73 2c 20 52 2e 2c 20 22 4d 61 74 68 65 6d 61 74 69 63 61 6c 20 54 68 65 6f 72 79 20 6f ises,.R.,."Mathematical.Theory.o
80540 66 20 50 72 6f 62 61 62 69 6c 69 74 79 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 61 6e 64 f.Probability................and
80560 20 53 74 61 74 69 73 74 69 63 73 22 2c 20 4e 65 77 20 59 6f 72 6b 3a 20 41 63 61 64 65 6d 69 63 .Statistics",.New.York:.Academic
80580 20 50 72 65 73 73 2c 20 31 39 36 34 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a .Press,.1964...........Examples.
805a0 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 ........--------.........Draw.sa
805c0 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 mples.from.the.distribution:....
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80600 20 6d 65 61 6e 20 61 6e 64 20 64 69 73 70 65 72 73 69 6f 6e 0a 20 20 20 20 20 20 20 20 3e 3e 3e .mean.and.dispersion.........>>>
80620 20 73 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 2e 76 6f 6e .s.=.np.random.default_rng().von
80640 6d 69 73 65 73 28 6d 75 2c 20 6b 61 70 70 61 2c 20 31 30 30 30 29 0a 0a 20 20 20 20 20 20 20 20 mises(mu,.kappa,.1000)..........
80660 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 20 6f 66 20 74 68 65 20 73 61 6d Display.the.histogram.of.the.sam
80680 70 6c 65 73 2c 20 61 6c 6f 6e 67 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 74 68 65 20 70 72 6f ples,.along.with.........the.pro
806a0 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 3a 0a 0a 20 20 20 20 bability.density.function:......
806c0 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 ....>>>.import.matplotlib.pyplot
806e0 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 73 63 69 70 79 2e 73 .as.plt.........>>>.from.scipy.s
80700 70 65 63 69 61 6c 20 69 6d 70 6f 72 74 20 69 30 20 20 23 20 64 6f 63 74 65 73 74 3a 20 2b 53 4b pecial.import.i0..#.doctest:.+SK
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80740 65 6e 73 69 74 79 3d 54 72 75 65 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 78 20 3d 20 6e 70 2e ensity=True).........>>>.x.=.np.
80760 6c 69 6e 73 70 61 63 65 28 2d 6e 70 2e 70 69 2c 20 6e 70 2e 70 69 2c 20 6e 75 6d 3d 35 31 29 0a linspace(-np.pi,.np.pi,.num=51).
80780 20 20 20 20 20 20 20 20 3e 3e 3e 20 79 20 3d 20 6e 70 2e 65 78 70 28 6b 61 70 70 61 2a 6e 70 2e ........>>>.y.=.np.exp(kappa*np.
807a0 63 6f 73 28 78 2d 6d 75 29 29 2f 28 32 2a 6e 70 2e 70 69 2a 69 30 28 6b 61 70 70 61 29 29 20 20 cos(x-mu))/(2*np.pi*i0(kappa))..
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80820 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 20 20 20 00 00 01 00 00 00 00 00 00 00 >.plt.show()....................
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80980 08 00 00 00 00 00 00 00 10 2e 09 80 01 00 00 00 0c c1 07 80 01 00 00 00 60 94 04 80 01 00 00 00 ........................`.......
809a0 03 00 00 00 00 00 00 00 60 de 07 80 01 00 00 00 e8 c1 07 80 01 00 00 00 10 2e 04 80 01 00 00 00 ........`.......................
809c0 03 00 00 00 00 00 00 00 20 63 08 80 01 00 00 00 f0 c1 07 80 01 00 00 00 20 1d 04 80 01 00 00 00 .........c......................
809e0 03 00 00 00 00 00 00 00 40 13 09 80 01 00 00 00 00 c2 07 80 01 00 00 00 e0 14 04 80 01 00 00 00 ........@.......................
80a00 03 00 00 00 00 00 00 00 d0 a0 09 80 01 00 00 00 08 c2 07 80 01 00 00 00 e0 10 04 80 01 00 00 00 ................................
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80a40 03 00 00 00 00 00 00 00 c0 f1 08 80 01 00 00 00 f4 c0 07 80 01 00 00 00 50 03 04 80 01 00 00 00 ........................P.......
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80b00 03 00 00 00 00 00 00 00 70 01 08 80 01 00 00 00 78 c2 07 80 01 00 00 00 60 e9 03 80 01 00 00 00 ........p.......x.......`.......
80b20 03 00 00 00 00 00 00 00 40 12 08 80 01 00 00 00 84 c2 07 80 01 00 00 00 60 e5 03 80 01 00 00 00 ........@...............`.......
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80b80 03 00 00 00 00 00 00 00 70 ed 07 80 01 00 00 00 a0 c2 07 80 01 00 00 00 00 d9 03 80 01 00 00 00 ........p.......................
80ba0 03 00 00 00 00 00 00 00 f0 d1 08 80 01 00 00 00 a8 c2 07 80 01 00 00 00 70 d4 03 80 01 00 00 00 ........................p.......
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80be0 03 00 00 00 00 00 00 00 20 4b 08 80 01 00 00 00 c0 c2 07 80 01 00 00 00 50 cb 03 80 01 00 00 00 .........K..............P.......
80c00 03 00 00 00 00 00 00 00 d0 fc 08 80 01 00 00 00 d0 c2 07 80 01 00 00 00 50 c7 03 80 01 00 00 00 ........................P.......
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80c80 03 00 00 00 00 00 00 00 e0 82 08 80 01 00 00 00 08 c3 07 80 01 00 00 00 f0 86 03 80 01 00 00 00 ................................
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80d00 03 00 00 00 00 00 00 00 90 56 08 80 01 00 00 00 40 c3 07 80 01 00 00 00 f0 76 03 80 01 00 00 00 .........V......@........v......
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80d40 03 00 00 00 00 00 00 00 70 d3 07 80 01 00 00 00 60 c3 07 80 01 00 00 00 60 5b 03 80 01 00 00 00 ........p.......`.......`[......
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80de0 03 00 00 00 00 00 00 00 e0 3b 09 80 01 00 00 00 c8 c3 07 80 01 00 00 00 60 73 02 80 01 00 00 00 .........;..............`s......
80e00 03 00 00 00 00 00 00 00 d0 5e 08 80 01 00 00 00 d0 c3 07 80 01 00 00 00 d0 47 02 80 01 00 00 00 .........^...............G......
80e20 03 00 00 00 00 00 00 00 f0 1b 09 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
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80e60 0a 20 20 20 20 20 20 20 20 69 6e 74 65 67 65 72 73 28 6c 6f 77 2c 20 68 69 67 68 3d 4e 6f 6e 65 .........integers(low,.high=None
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80f40 20 52 65 70 6c 61 63 65 73 0a 20 20 20 20 20 20 20 20 60 52 61 6e 64 6f 6d 53 74 61 74 65 2e 72 .Replaces.........`RandomState.r
80f60 61 6e 64 69 6e 74 60 20 28 77 69 74 68 20 65 6e 64 70 6f 69 6e 74 3d 46 61 6c 73 65 29 20 61 6e andint`.(with.endpoint=False).an
80f80 64 0a 20 20 20 20 20 20 20 20 60 52 61 6e 64 6f 6d 53 74 61 74 65 2e 72 61 6e 64 6f 6d 5f 69 6e d.........`RandomState.random_in
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80fc0 20 20 20 20 20 20 52 65 74 75 72 6e 20 72 61 6e 64 6f 6d 20 69 6e 74 65 67 65 72 73 20 66 72 6f ......Return.random.integers.fro
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810c0 20 20 20 20 20 20 20 20 20 20 20 20 4c 6f 77 65 73 74 20 28 73 69 67 6e 65 64 29 20 69 6e 74 65 ............Lowest.(signed).inte
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81160 20 20 20 20 20 20 20 20 20 20 75 73 65 64 20 66 6f 72 20 60 68 69 67 68 60 29 2e 0a 20 20 20 20 ..........used.for.`high`)......
81180 20 20 20 20 68 69 67 68 20 3a 20 69 6e 74 20 6f 72 20 61 72 72 61 79 2d 6c 69 6b 65 20 6f 66 20 ....high.:.int.or.array-like.of.
811a0 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 70 72 ints,.optional.............If.pr
811c0 6f 76 69 64 65 64 2c 20 6f 6e 65 20 61 62 6f 76 65 20 74 68 65 20 6c 61 72 67 65 73 74 20 28 73 ovided,.one.above.the.largest.(s
811e0 69 67 6e 65 64 29 20 69 6e 74 65 67 65 72 20 74 6f 20 62 65 20 64 72 61 77 6e 0a 20 20 20 20 20 igned).integer.to.be.drawn......
81200 20 20 20 20 20 20 20 66 72 6f 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 28 73 65 .......from.the.distribution.(se
81220 65 20 61 62 6f 76 65 20 66 6f 72 20 62 65 68 61 76 69 6f 72 20 69 66 20 60 60 68 69 67 68 3d 4e e.above.for.behavior.if.``high=N
81240 6f 6e 65 60 60 29 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 61 72 72 61 79 2d 6c 69 6b one``)..............If.array-lik
81260 65 2c 20 6d 75 73 74 20 63 6f 6e 74 61 69 6e 20 69 6e 74 65 67 65 72 20 76 61 6c 75 65 73 0a 20 e,.must.contain.integer.values..
81280 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e .......size.:.int.or.tuple.of.in
812a0 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 ts,.optional.............Output.
812c0 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 shape...If.the.given.shape.is,.e
812e0 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 .g.,.``(m,.n,.k)``,.then........
81300 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 .....``m.*.n.*.k``.samples.are.d
81320 72 61 77 6e 2e 20 20 44 65 66 61 75 6c 74 20 69 73 20 4e 6f 6e 65 2c 20 69 6e 20 77 68 69 63 68 rawn...Default.is.None,.in.which
81340 20 63 61 73 65 20 61 0a 20 20 20 20 20 20 20 20 20 20 20 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 .case.a.............single.value
81360 20 69 73 20 72 65 74 75 72 6e 65 64 2e 0a 20 20 20 20 20 20 20 20 64 74 79 70 65 20 3a 20 64 74 .is.returned..........dtype.:.dt
81380 79 70 65 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 65 73 69 72 65 ype,.optional.............Desire
813a0 64 20 64 74 79 70 65 20 6f 66 20 74 68 65 20 72 65 73 75 6c 74 2e 20 42 79 74 65 6f 72 64 65 72 d.dtype.of.the.result..Byteorder
813c0 20 6d 75 73 74 20 62 65 20 6e 61 74 69 76 65 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 54 68 65 .must.be.native..............The
813e0 20 64 65 66 61 75 6c 74 20 76 61 6c 75 65 20 69 73 20 6e 70 2e 69 6e 74 36 34 2e 0a 20 20 20 20 .default.value.is.np.int64......
81400 20 20 20 20 65 6e 64 70 6f 69 6e 74 20 3a 20 62 6f 6f 6c 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 ....endpoint.:.bool,.optional...
81420 20 20 20 20 20 20 20 20 20 20 49 66 20 74 72 75 65 2c 20 73 61 6d 70 6c 65 20 66 72 6f 6d 20 74 ..........If.true,.sample.from.t
81440 68 65 20 69 6e 74 65 72 76 61 6c 20 5b 6c 6f 77 2c 20 68 69 67 68 5d 20 69 6e 73 74 65 61 64 20 he.interval.[low,.high].instead.
81460 6f 66 20 74 68 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 64 65 66 61 75 6c 74 20 5b 6c 6f 77 2c of.the.............default.[low,
81480 20 68 69 67 68 29 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 65 66 61 75 6c 74 73 20 74 6f 20 46 .high).............Defaults.to.F
814a0 61 6c 73 65 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d alse..........Returns.........--
814c0 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 69 6e 74 20 6f 72 20 6e 64 61 72 72 -----.........out.:.int.or.ndarr
814e0 61 79 20 6f 66 20 69 6e 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 73 69 7a 65 60 2d 73 68 ay.of.ints.............`size`-sh
81500 61 70 65 64 20 61 72 72 61 79 20 6f 66 20 72 61 6e 64 6f 6d 20 69 6e 74 65 67 65 72 73 20 66 72 aped.array.of.random.integers.fr
81520 6f 6d 20 74 68 65 20 61 70 70 72 6f 70 72 69 61 74 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 64 om.the.appropriate.............d
81540 69 73 74 72 69 62 75 74 69 6f 6e 2c 20 6f 72 20 61 20 73 69 6e 67 6c 65 20 73 75 63 68 20 72 61 istribution,.or.a.single.such.ra
81560 6e 64 6f 6d 20 69 6e 74 20 69 66 20 60 73 69 7a 65 60 20 6e 6f 74 20 70 72 6f 76 69 64 65 64 2e ndom.int.if.`size`.not.provided.
81580 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 ..........Notes.........-----...
815a0 20 20 20 20 20 20 57 68 65 6e 20 75 73 69 6e 67 20 62 72 6f 61 64 63 61 73 74 69 6e 67 20 77 69 ......When.using.broadcasting.wi
815c0 74 68 20 75 69 6e 74 36 34 20 64 74 79 70 65 73 2c 20 74 68 65 20 6d 61 78 69 6d 75 6d 20 76 61 th.uint64.dtypes,.the.maximum.va
815e0 6c 75 65 20 28 32 2a 2a 36 34 29 0a 20 20 20 20 20 20 20 20 63 61 6e 6e 6f 74 20 62 65 20 72 65 lue.(2**64).........cannot.be.re
81600 70 72 65 73 65 6e 74 65 64 20 61 73 20 61 20 73 74 61 6e 64 61 72 64 20 69 6e 74 65 67 65 72 20 presented.as.a.standard.integer.
81620 74 79 70 65 2e 20 54 68 65 20 68 69 67 68 20 61 72 72 61 79 20 28 6f 72 0a 20 20 20 20 20 20 20 type..The.high.array.(or........
81640 20 6c 6f 77 20 69 66 20 68 69 67 68 20 69 73 20 4e 6f 6e 65 29 20 6d 75 73 74 20 68 61 76 65 20 .low.if.high.is.None).must.have.
81660 6f 62 6a 65 63 74 20 64 74 79 70 65 2c 20 65 2e 67 2e 2c 20 61 72 72 61 79 28 5b 32 2a 2a 36 34 object.dtype,.e.g.,.array([2**64
81680 5d 29 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d ])...........Examples.........--
816a0 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 20 3d 20 6e 70 2e 72 61 6e 64 ------.........>>>.rng.=.np.rand
816c0 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 om.default_rng().........>>>.rng
816e0 2e 69 6e 74 65 67 65 72 73 28 32 2c 20 73 69 7a 65 3d 31 30 29 0a 20 20 20 20 20 20 20 20 61 72 .integers(2,.size=10).........ar
81700 72 61 79 28 5b 31 2c 20 30 2c 20 30 2c 20 30 2c 20 31 2c 20 31 2c 20 30 2c 20 30 2c 20 31 2c 20 ray([1,.0,.0,.0,.1,.1,.0,.0,.1,.
81720 30 5d 29 20 20 23 20 72 61 6e 64 6f 6d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 69 6e 0])..#.random.........>>>.rng.in
81740 74 65 67 65 72 73 28 31 2c 20 73 69 7a 65 3d 31 30 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 tegers(1,.size=10).........array
81760 28 5b 30 2c 20 30 2c 20 30 2c 20 30 2c 20 30 2c 20 30 2c 20 30 2c 20 30 2c 20 30 2c 20 30 5d 29 ([0,.0,.0,.0,.0,.0,.0,.0,.0,.0])
81780 0a 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 74 65 20 61 20 32 20 78 20 34 20 61 72 72 61 79 ..........Generate.a.2.x.4.array
817a0 20 6f 66 20 69 6e 74 73 20 62 65 74 77 65 65 6e 20 30 20 61 6e 64 20 34 2c 20 69 6e 63 6c 75 73 .of.ints.between.0.and.4,.inclus
817c0 69 76 65 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 35 ive:..........>>>.rng.integers(5
817e0 2c 20 73 69 7a 65 3d 28 32 2c 20 34 29 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 5b 34 ,.size=(2,.4)).........array([[4
81800 2c 20 30 2c 20 32 2c 20 31 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5b 33 2c 20 32 ,.0,.2,.1],................[3,.2
81820 2c 20 32 2c 20 30 5d 5d 29 20 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 47 65 6e ,.2,.0]])..#.random..........Gen
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81860 72 65 6e 74 20 75 70 70 65 72 20 62 6f 75 6e 64 73 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 rent.upper.bounds..........>>>.r
81880 6e 67 2e 69 6e 74 65 67 65 72 73 28 31 2c 20 5b 33 2c 20 35 2c 20 31 30 5d 29 0a 20 20 20 20 20 ng.integers(1,.[3,.5,.10])......
818a0 20 20 20 61 72 72 61 79 28 5b 32 2c 20 32 2c 20 39 5d 29 20 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 ...array([2,.2,.9])..#.random...
818c0 20 20 20 20 20 20 20 47 65 6e 65 72 61 74 65 20 61 20 31 20 62 79 20 33 20 61 72 72 61 79 20 77 .......Generate.a.1.by.3.array.w
818e0 69 74 68 20 33 20 64 69 66 66 65 72 65 6e 74 20 6c 6f 77 65 72 20 62 6f 75 6e 64 73 0a 0a 20 20 ith.3.different.lower.bounds....
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81920 2c 20 31 30 29 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b 39 2c 20 38 2c 20 37 5d 29 20 20 ,.10).........array([9,.8,.7])..
81940 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 74 65 20 61 20 32 20 62 #.random..........Generate.a.2.b
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81980 68 20 64 74 79 70 65 20 6f 66 20 75 69 6e 74 38 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e h.dtype.of.uint8..........>>>.rn
819a0 67 2e 69 6e 74 65 67 65 72 73 28 5b 31 2c 20 33 2c 20 35 2c 20 37 5d 2c 20 5b 5b 31 30 5d 2c 20 g.integers([1,.3,.5,.7],.[[10],.
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81a40 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 nces.........----------.........
81a60 2e 2e 20 5b 31 5d 20 44 61 6e 69 65 6c 20 4c 65 6d 69 72 65 2e 2c 20 22 46 61 73 74 20 52 61 6e ...[1].Daniel.Lemire.,."Fast.Ran
81a80 64 6f 6d 20 49 6e 74 65 67 65 72 20 47 65 6e 65 72 61 74 69 6f 6e 20 69 6e 20 61 6e 20 49 6e 74 dom.Integer.Generation.in.an.Int
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81ae0 20 53 69 6d 75 6c 61 74 69 6f 6e 20 32 39 20 28 31 29 2c 20 32 30 31 39 2c 0a 20 20 20 20 20 20 .Simulation.29.(1),.2019,.......
81b00 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 61 72 78 69 76 2e 6f 72 67 2f 61 62 73 2f 31 38 .........http://arxiv.org/abs/18
81b20 30 35 2e 31 30 39 34 31 2e 0a 0a 20 20 20 20 20 20 20 20 00 00 00 00 00 00 00 00 00 00 00 00 00 05.10941........................
81b40 0a 20 20 20 20 20 20 20 20 65 78 70 6f 6e 65 6e 74 69 61 6c 28 73 63 61 6c 65 3d 31 2e 30 2c 20 .........exponential(scale=1.0,.
81b60 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 size=None)..........Draw.samples
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81be0 3a 3a 20 66 28 78 3b 20 5c 66 72 61 63 7b 31 7d 7b 5c 62 65 74 61 7d 29 20 3d 20 5c 66 72 61 63 ::.f(x;.\frac{1}{\beta}).=.\frac
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81c20 29 2c 0a 0a 20 20 20 20 20 20 20 20 66 6f 72 20 60 60 78 20 3e 20 30 60 60 20 61 6e 64 20 30 20 ),..........for.``x.>.0``.and.0.
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81cc0 20 20 20 20 20 20 20 54 68 65 20 72 61 74 65 20 70 61 72 61 6d 65 74 65 72 20 69 73 20 61 6e 20 .......The.rate.parameter.is.an.
81ce0 61 6c 74 65 72 6e 61 74 69 76 65 2c 20 77 69 64 65 6c 79 20 75 73 65 64 20 70 61 72 61 6d 65 74 alternative,.widely.used.paramet
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81d80 20 20 20 20 20 20 67 65 6f 6d 65 74 72 69 63 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 20 49 ......geometric.distribution...I
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81de0 72 61 69 6e 64 72 6f 70 73 20 6d 65 61 73 75 72 65 64 20 6f 76 65 72 20 6d 61 6e 79 20 72 61 69 raindrops.measured.over.many.rai
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81ea0 20 20 20 20 20 20 20 20 20 20 20 20 54 68 65 20 73 63 61 6c 65 20 70 61 72 61 6d 65 74 65 72 2c ............The.scale.parameter,
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81f20 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 s,.optional.............Output.s
81f40 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e hape...If.the.given.shape.is,.e.
81f60 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 g.,.``(m,.n,.k)``,.then.........
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81fa0 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 awn...If.size.is.``None``.(defau
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82000 61 6c 61 72 2e 20 20 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 alar...Otherwise,.............``
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82040 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 re.drawn...........Returns......
82060 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 ...-------.........out.:.ndarray
82080 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d .or.scalar.............Drawn.sam
820a0 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 65 78 70 6f ples.from.the.parameterized.expo
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820e0 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 eferences.........----------....
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82120 2e 2c 20 22 50 72 6f 62 61 62 69 6c 69 74 79 2c 20 52 61 6e 64 6f 6d 20 56 61 72 69 61 62 6c 65 .,."Probability,.Random.Variable
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82180 20 35 37 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 .57.............[2].Wikipedia,."
821a0 50 6f 69 73 73 6f 6e 20 70 72 6f 63 65 73 73 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 Poisson.process",...............
821c0 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 50 .https://en.wikipedia.org/wiki/P
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82200 6b 69 70 65 64 69 61 2c 20 22 45 78 70 6f 6e 65 6e 74 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 kipedia,."Exponential.distributi
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82280 0a 20 20 20 20 20 20 20 20 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 28 6e 67 6f 6f 64 2c 20 6e .........hypergeometric(ngood,.n
822a0 62 61 64 2c 20 6e 73 61 6d 70 6c 65 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 bad,.nsample,.size=None)........
822c0 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 48 79 70 65 72 67 65 6f 6d 65 ..Draw.samples.from.a.Hypergeome
822e0 74 72 69 63 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 61 6d 70 tric.distribution...........Samp
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82340 20 20 20 20 20 20 20 20 70 61 72 61 6d 65 74 65 72 73 2c 20 60 6e 67 6f 6f 64 60 20 28 77 61 79 ........parameters,.`ngood`.(way
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82520 62 61 64 20 73 65 6c 65 63 74 69 6f 6e 2e 20 20 4d 75 73 74 20 62 65 20 6e 6f 6e 6e 65 67 61 74 bad.selection...Must.be.nonnegat
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825c0 6f 6e 6e 65 67 61 74 69 76 65 20 61 6e 64 20 6c 65 73 73 20 74 68 61 6e 0a 20 20 20 20 20 20 20 onnegative.and.less.than........
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828c0 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 ....See.Also.........--------...
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82f80 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d ....References.........---------
82fa0 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 4c 65 6e 74 6e 65 72 2c 20 4d 61 72 76 69 6e -............[1].Lentner,.Marvin
82fc0 2c 20 22 45 6c 65 6d 65 6e 74 61 72 79 20 41 70 70 6c 69 65 64 20 53 74 61 74 69 73 74 69 63 73 ,."Elementary.Applied.Statistics
82fe0 22 2c 20 42 6f 67 64 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 61 6e 64 20 51 75 69 ",.Bogden................and.Qui
83000 67 6c 65 79 2c 20 31 39 37 32 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 65 69 73 73 gley,.1972.............[2].Weiss
83020 74 65 69 6e 2c 20 45 72 69 63 20 57 2e 20 22 48 79 70 65 72 67 65 6f 6d 65 74 72 69 63 20 44 69 tein,.Eric.W.."Hypergeometric.Di
83040 73 74 72 69 62 75 74 69 6f 6e 2e 22 20 46 72 6f 6d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 stribution.".From...............
83060 20 4d 61 74 68 57 6f 72 6c 64 2d 2d 41 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 65 73 6f 75 72 .MathWorld--A.Wolfram.Web.Resour
83080 63 65 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d 61 74 68 77 6f ce.................http://mathwo
830a0 72 6c 64 2e 77 6f 6c 66 72 61 6d 2e 63 6f 6d 2f 48 79 70 65 72 67 65 6f 6d 65 74 72 69 63 44 69 rld.wolfram.com/HypergeometricDi
830c0 73 74 72 69 62 75 74 69 6f 6e 2e 68 74 6d 6c 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 33 5d 20 57 stribution.html............[3].W
830e0 69 6b 69 70 65 64 69 61 2c 20 22 48 79 70 65 72 67 65 6f 6d 65 74 72 69 63 20 64 69 73 74 72 69 ikipedia,."Hypergeometric.distri
83100 62 75 74 69 6f 6e 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f bution",................https://
83120 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 48 79 70 65 72 67 65 6f 6d 65 en.wikipedia.org/wiki/Hypergeome
83140 74 72 69 63 5f 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 34 5d tric_distribution............[4]
83160 20 53 74 61 64 6c 6f 62 65 72 2c 20 45 72 6e 73 74 2c 20 22 54 68 65 20 72 61 74 69 6f 20 6f 66 .Stadlober,.Ernst,."The.ratio.of
83180 20 75 6e 69 66 6f 72 6d 73 20 61 70 70 72 6f 61 63 68 20 66 6f 72 20 67 65 6e 65 72 61 74 69 6e .uniforms.approach.for.generatin
831a0 67 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 64 69 73 63 72 65 74 65 20 72 61 6e 64 6f 6d g................discrete.random
831c0 20 76 61 72 69 61 74 65 73 22 2c 20 4a 6f 75 72 6e 61 6c 20 6f 66 20 43 6f 6d 70 75 74 61 74 69 .variates",.Journal.of.Computati
831e0 6f 6e 61 6c 20 61 6e 64 20 41 70 70 6c 69 65 64 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 onal.and.Applied................
83200 4d 61 74 68 65 6d 61 74 69 63 73 2c 20 33 31 2c 20 70 70 2e 20 31 38 31 2d 31 38 39 20 28 31 39 Mathematics,.31,.pp..181-189.(19
83220 39 30 29 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 90)...........Examples.........-
83240 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f -------.........Draw.samples.fro
83260 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e m.the.distribution:..........>>>
83280 20 72 6e 67 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 .rng.=.np.random.default_rng()..
832a0 20 20 20 20 20 20 20 3e 3e 3e 20 6e 67 6f 6f 64 2c 20 6e 62 61 64 2c 20 6e 73 61 6d 70 20 3d 20 .......>>>.ngood,.nbad,.nsamp.=.
832c0 31 30 30 2c 20 32 2c 20 31 30 0a 20 20 20 20 20 20 20 20 23 20 6e 75 6d 62 65 72 20 6f 66 20 67 100,.2,.10.........#.number.of.g
832e0 6f 6f 64 2c 20 6e 75 6d 62 65 72 20 6f 66 20 62 61 64 2c 20 61 6e 64 20 6e 75 6d 62 65 72 20 6f ood,.number.of.bad,.and.number.o
83300 66 20 73 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 72 6e 67 2e 68 79 f.samples.........>>>.s.=.rng.hy
83320 70 65 72 67 65 6f 6d 65 74 72 69 63 28 6e 67 6f 6f 64 2c 20 6e 62 61 64 2c 20 6e 73 61 6d 70 2c pergeometric(ngood,.nbad,.nsamp,
83340 20 31 30 30 30 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6d 61 74 70 6c 6f 74 6c .1000).........>>>.from.matplotl
83360 69 62 2e 70 79 70 6c 6f 74 20 69 6d 70 6f 72 74 20 68 69 73 74 0a 20 20 20 20 20 20 20 20 3e 3e ib.pyplot.import.hist.........>>
83380 3e 20 68 69 73 74 28 73 29 0a 20 20 20 20 20 20 20 20 23 20 20 20 6e 6f 74 65 20 74 68 61 74 20 >.hist(s).........#...note.that.
833a0 69 74 20 69 73 20 76 65 72 79 20 75 6e 6c 69 6b 65 6c 79 20 74 6f 20 67 72 61 62 20 62 6f 74 68 it.is.very.unlikely.to.grab.both
833c0 20 62 61 64 20 69 74 65 6d 73 0a 0a 20 20 20 20 20 20 20 20 53 75 70 70 6f 73 65 20 79 6f 75 20 .bad.items..........Suppose.you.
833e0 68 61 76 65 20 61 6e 20 75 72 6e 20 77 69 74 68 20 31 35 20 77 68 69 74 65 20 61 6e 64 20 31 35 have.an.urn.with.15.white.and.15
83400 20 62 6c 61 63 6b 20 6d 61 72 62 6c 65 73 2e 0a 20 20 20 20 20 20 20 20 49 66 20 79 6f 75 20 70 .black.marbles..........If.you.p
83420 75 6c 6c 20 31 35 20 6d 61 72 62 6c 65 73 20 61 74 20 72 61 6e 64 6f 6d 2c 20 68 6f 77 20 6c 69 ull.15.marbles.at.random,.how.li
83440 6b 65 6c 79 20 69 73 20 69 74 20 74 68 61 74 0a 20 20 20 20 20 20 20 20 31 32 20 6f 72 20 6d 6f kely.is.it.that.........12.or.mo
83460 72 65 20 6f 66 20 74 68 65 6d 20 61 72 65 20 6f 6e 65 20 63 6f 6c 6f 72 3f 0a 0a 20 20 20 20 20 re.of.them.are.one.color?.......
83480 20 20 20 3e 3e 3e 20 73 20 3d 20 72 6e 67 2e 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 28 31 35 ...>>>.s.=.rng.hypergeometric(15
834a0 2c 20 31 35 2c 20 31 35 2c 20 31 30 30 30 30 30 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 75 ,.15,.15,.100000).........>>>.su
834c0 6d 28 73 3e 3d 31 32 29 2f 31 30 30 30 30 30 2e 20 2b 20 73 75 6d 28 73 3c 3d 33 29 2f 31 30 30 m(s>=12)/100000..+.sum(s<=3)/100
834e0 30 30 30 2e 0a 20 20 20 20 20 20 20 20 23 20 20 20 61 6e 73 77 65 72 20 3d 20 30 2e 30 30 33 20 000..........#...answer.=.0.003.
83500 2e 2e 2e 20 70 72 65 74 74 79 20 75 6e 6c 69 6b 65 6c 79 21 0a 0a 20 20 20 20 20 20 20 20 00 00 ....pretty.unlikely!............
83520 0a 20 20 20 20 20 20 20 20 6c 6f 67 69 73 74 69 63 28 6c 6f 63 3d 30 2e 30 2c 20 73 63 61 6c 65 .........logistic(loc=0.0,.scale
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83c20 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b .........----------............[
83c40 31 5d 20 52 65 69 73 73 2c 20 52 2e 2d 44 2e 20 61 6e 64 20 54 68 6f 6d 61 73 20 4d 2e 20 28 32 1].Reiss,.R.-D..and.Thomas.M..(2
83c60 30 30 31 29 2c 20 22 53 74 61 74 69 73 74 69 63 61 6c 20 41 6e 61 6c 79 73 69 73 20 6f 66 0a 20 001),."Statistical.Analysis.of..
83c80 20 20 20 20 20 20 20 20 20 20 20 20 20 20 45 78 74 72 65 6d 65 20 56 61 6c 75 65 73 2c 20 66 72 ..............Extreme.Values,.fr
83ca0 6f 6d 20 49 6e 73 75 72 61 6e 63 65 2c 20 46 69 6e 61 6e 63 65 2c 20 48 79 64 72 6f 6c 6f 67 79 om.Insurance,.Finance,.Hydrology
83cc0 20 61 6e 64 20 4f 74 68 65 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 46 69 65 6c 64 73 .and.Other................Fields
83ce0 2c 22 20 42 69 72 6b 68 61 75 73 65 72 20 56 65 72 6c 61 67 2c 20 42 61 73 65 6c 2c 20 70 70 20 ,".Birkhauser.Verlag,.Basel,.pp.
83d00 31 33 32 2d 31 33 33 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 65 69 73 73 74 65 69 132-133.............[2].Weisstei
83d20 6e 2c 20 45 72 69 63 20 57 2e 20 22 4c 6f 67 69 73 74 69 63 20 44 69 73 74 72 69 62 75 74 69 6f n,.Eric.W.."Logistic.Distributio
83d40 6e 2e 22 20 46 72 6f 6d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 4d 61 74 68 57 6f 72 6c n.".From................MathWorl
83d60 64 2d 2d 41 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 65 73 6f 75 72 63 65 2e 0a 20 20 20 20 20 d--A.Wolfram.Web.Resource.......
83d80 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d 61 74 68 77 6f 72 6c 64 2e 77 6f 6c 66 72 ..........http://mathworld.wolfr
83da0 61 6d 2e 63 6f 6d 2f 4c 6f 67 69 73 74 69 63 44 69 73 74 72 69 62 75 74 69 6f 6e 2e 68 74 6d 6c am.com/LogisticDistribution.html
83dc0 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 33 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 4c 6f 67 69 ............[3].Wikipedia,."Logi
83de0 73 74 69 63 2d 64 69 73 74 72 69 62 75 74 69 6f 6e 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 stic-distribution",.............
83e00 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 ...https://en.wikipedia.org/wiki
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83e40 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 Examples.........--------.......
83e60 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 ..Draw.samples.from.the.distribu
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83f00 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e plotlib.pyplot.as.plt.........>>
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847c0 20 52 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .R..............................
847e0 b8 cc 07 80 01 00 00 00 10 52 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .........R......................
84800 00 00 00 00 00 00 00 00 c4 cc 07 80 01 00 00 00 c0 51 01 80 01 00 00 00 00 00 00 00 00 00 00 00 .................Q..............
84820 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 d0 cc 07 80 01 00 00 00 80 51 01 80 01 00 00 00 .........................Q......
84840 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 dc cc 07 80 01 00 00 00 ................................
84860 70 50 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 pP..............................
84880 e4 cc 07 80 01 00 00 00 00 4f 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .........O......................
848a0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
848c0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 73 68 75 66 66 6c 65 .........................shuffle
848e0 28 78 2c 20 61 78 69 73 3d 30 29 0a 0a 20 20 20 20 20 20 20 20 4d 6f 64 69 66 79 20 61 6e 20 61 (x,.axis=0)..........Modify.an.a
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84960 20 62 75 74 20 74 68 65 69 72 20 63 6f 6e 74 65 6e 74 73 20 72 65 6d 61 69 6e 73 20 74 68 65 20 .but.their.contents.remains.the.
84980 73 61 6d 65 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 same...........Parameters.......
849a0 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 78 20 3a 20 6e 64 61 72 72 61 79 ..----------.........x.:.ndarray
849c0 20 6f 72 20 4d 75 74 61 62 6c 65 53 65 71 75 65 6e 63 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 .or.MutableSequence.............
849e0 54 68 65 20 61 72 72 61 79 2c 20 6c 69 73 74 20 6f 72 20 6d 75 74 61 62 6c 65 20 73 65 71 75 65 The.array,.list.or.mutable.seque
84a00 6e 63 65 20 74 6f 20 62 65 20 73 68 75 66 66 6c 65 64 2e 0a 20 20 20 20 20 20 20 20 61 78 69 73 nce.to.be.shuffled..........axis
84a20 20 3a 20 69 6e 74 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 54 68 65 .:.int,.optional.............The
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84a60 67 2e 20 44 65 66 61 75 6c 74 20 69 73 20 30 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 74 20 g..Default.is.0..............It.
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84aa0 62 6a 65 63 74 73 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 bjects...........Returns........
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84ae0 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 xamples.........--------........
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84b60 20 20 20 20 20 20 20 20 3e 3e 3e 20 61 72 72 0a 20 20 20 20 20 20 20 20 5b 31 20 37 20 35 20 32 ........>>>.arr.........[1.7.5.2
84b80 20 39 20 34 20 33 20 36 20 30 20 38 5d 20 23 20 72 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 .9.4.3.6.0.8].#.random..........
84ba0 3e 3e 3e 20 61 72 72 20 3d 20 6e 70 2e 61 72 61 6e 67 65 28 39 29 2e 72 65 73 68 61 70 65 28 28 >>>.arr.=.np.arange(9).reshape((
84bc0 33 2c 20 33 29 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 73 68 75 66 66 6c 65 28 61 3,.3)).........>>>.rng.shuffle(a
84be0 72 72 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 61 72 72 0a 20 20 20 20 20 20 20 20 61 72 72 61 rr).........>>>.arr.........arra
84c00 79 28 5b 5b 33 2c 20 34 2c 20 35 5d 2c 20 23 20 72 61 6e 64 6f 6d 0a 20 20 20 20 20 20 20 20 20 y([[3,.4,.5],.#.random..........
84c20 20 20 20 20 20 20 5b 36 2c 20 37 2c 20 38 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 ......[6,.7,.8],................
84c40 5b 30 2c 20 31 2c 20 32 5d 5d 29 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 61 72 72 20 3d 20 6e [0,.1,.2]])..........>>>.arr.=.n
84c60 70 2e 61 72 61 6e 67 65 28 39 29 2e 72 65 73 68 61 70 65 28 28 33 2c 20 33 29 29 0a 20 20 20 20 p.arange(9).reshape((3,.3)).....
84c80 20 20 20 20 3e 3e 3e 20 72 6e 67 2e 73 68 75 66 66 6c 65 28 61 72 72 2c 20 61 78 69 73 3d 31 29 ....>>>.rng.shuffle(arr,.axis=1)
84ca0 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 61 72 72 0a 20 20 20 20 20 20 20 20 61 72 72 61 79 28 5b .........>>>.arr.........array([
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84d00 20 36 2c 20 37 5d 5d 29 0a 20 20 20 20 20 20 20 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .6,.7]])........................
84d20 0a 20 20 20 20 20 20 20 20 75 6e 69 66 6f 72 6d 28 6c 6f 77 3d 30 2e 30 2c 20 68 69 67 68 3d 31 .........uniform(low=0.0,.high=1
84d40 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d .0,.size=None)..........Draw.sam
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84d80 2e 0a 0a 20 20 20 20 20 20 20 20 53 61 6d 70 6c 65 73 20 61 72 65 20 75 6e 69 66 6f 72 6d 6c 79 ...........Samples.are.uniformly
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84dc0 69 6e 74 65 72 76 61 6c 0a 20 20 20 20 20 20 20 20 60 60 5b 6c 6f 77 2c 20 68 69 67 68 29 60 60 interval.........``[low,.high)``
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84e60 20 20 20 20 20 20 20 62 79 20 60 75 6e 69 66 6f 72 6d 60 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 .......by.`uniform`...........Pa
84e80 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 rameters.........----------.....
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84ec0 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4c 6f .floats,.optional.............Lo
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84f00 76 61 6c 2e 20 20 41 6c 6c 20 76 61 6c 75 65 73 20 67 65 6e 65 72 61 74 65 64 20 77 69 6c 6c 20 val...All.values.generated.will.
84f20 62 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 67 72 65 61 74 65 72 20 74 68 61 6e 20 6f 72 20 65 be.............greater.than.or.e
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84f80 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 55 ray_like.of.floats.............U
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84fc0 72 76 61 6c 2e 20 20 41 6c 6c 20 76 61 6c 75 65 73 20 67 65 6e 65 72 61 74 65 64 20 77 69 6c 6c rval...All.values.generated.will
84fe0 20 62 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 6c 65 73 73 20 74 68 61 6e 20 68 69 67 68 2e 20 .be.............less.than.high..
85000 20 54 68 65 20 68 69 67 68 20 6c 69 6d 69 74 20 6d 61 79 20 62 65 20 69 6e 63 6c 75 64 65 64 20 .The.high.limit.may.be.included.
85020 69 6e 20 74 68 65 20 72 65 74 75 72 6e 65 64 20 61 72 72 61 79 20 6f 66 20 0a 20 20 20 20 20 20 in.the.returned.array.of........
85040 20 20 20 20 20 20 66 6c 6f 61 74 73 20 64 75 65 20 74 6f 20 66 6c 6f 61 74 69 6e 67 2d 70 6f 69 ......floats.due.to.floating-poi
85060 6e 74 20 72 6f 75 6e 64 69 6e 67 20 69 6e 20 74 68 65 20 65 71 75 61 74 69 6f 6e 20 0a 20 20 20 nt.rounding.in.the.equation.....
85080 20 20 20 20 20 20 20 20 20 60 60 6c 6f 77 20 2b 20 28 68 69 67 68 2d 6c 6f 77 29 20 2a 20 72 61 .........``low.+.(high-low).*.ra
850a0 6e 64 6f 6d 5f 73 61 6d 70 6c 65 28 29 60 60 2e 20 20 68 69 67 68 20 2d 20 6c 6f 77 20 6d 75 73 ndom_sample()``...high.-.low.mus
850c0 74 20 62 65 20 0a 20 20 20 20 20 20 20 20 20 20 20 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 2e 20 t.be..............non-negative..
850e0 20 54 68 65 20 64 65 66 61 75 6c 74 20 76 61 6c 75 65 20 69 73 20 31 2e 30 2e 0a 20 20 20 20 20 .The.default.value.is.1.0.......
85100 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 ...size.:.int.or.tuple.of.ints,.
85120 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 optional.............Output.shap
85140 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c e...If.the.given.shape.is,.e.g.,
85160 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 .``(m,.n,.k)``,.then............
85180 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e .``m.*.n.*.k``.samples.are.drawn
851a0 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 ...If.size.is.``None``.(default)
851c0 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 ,.............a.single.value.is.
851e0 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 6c 6f 77 60 60 20 61 6e 64 20 60 60 68 69 67 68 60 60 returned.if.``low``.and.``high``
85200 20 61 72 65 20 62 6f 74 68 20 73 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f .are.both.scalars..............O
85220 74 68 65 72 77 69 73 65 2c 20 60 60 6e 70 2e 62 72 6f 61 64 63 61 73 74 28 6c 6f 77 2c 20 68 69 therwise,.``np.broadcast(low,.hi
85240 67 68 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 gh).size``.samples.are.drawn....
85260 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 .......Returns.........-------..
85280 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 .......out.:.ndarray.or.scalar..
852a0 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 ...........Drawn.samples.from.th
852c0 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 75 6e 69 66 6f 72 6d 20 64 69 73 74 72 69 62 75 e.parameterized.uniform.distribu
852e0 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 tion...........See.Also.........
85300 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 69 6e 74 65 67 65 72 73 20 3a 20 44 69 73 63 --------.........integers.:.Disc
85320 72 65 74 65 20 75 6e 69 66 6f 72 6d 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 20 79 69 65 6c 64 rete.uniform.distribution,.yield
85340 69 6e 67 20 69 6e 74 65 67 65 72 73 2e 0a 20 20 20 20 20 20 20 20 72 61 6e 64 6f 6d 20 3a 20 46 ing.integers..........random.:.F
85360 6c 6f 61 74 73 20 75 6e 69 66 6f 72 6d 6c 79 20 64 69 73 74 72 69 62 75 74 65 64 20 6f 76 65 72 loats.uniformly.distributed.over
85380 20 60 60 5b 30 2c 20 31 29 60 60 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 .``[0,.1)``...........Notes.....
853a0 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 ....-----.........The.probabilit
853c0 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 74 68 65 20 75 6e 69 66 6f 72 y.density.function.of.the.unifor
853e0 6d 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 m.distribution.is.............ma
85400 74 68 3a 3a 20 70 28 78 29 20 3d 20 5c 66 72 61 63 7b 31 7d 7b 62 20 2d 20 61 7d 0a 0a 20 20 20 th::.p(x).=.\frac{1}{b.-.a}.....
85420 20 20 20 20 20 61 6e 79 77 68 65 72 65 20 77 69 74 68 69 6e 20 74 68 65 20 69 6e 74 65 72 76 61 .....anywhere.within.the.interva
85440 6c 20 60 60 5b 61 2c 20 62 29 60 60 2c 20 61 6e 64 20 7a 65 72 6f 20 65 6c 73 65 77 68 65 72 65 l.``[a,.b)``,.and.zero.elsewhere
85460 2e 0a 0a 20 20 20 20 20 20 20 20 57 68 65 6e 20 60 60 68 69 67 68 60 60 20 3d 3d 20 60 60 6c 6f ...........When.``high``.==.``lo
85480 77 60 60 2c 20 76 61 6c 75 65 73 20 6f 66 20 60 60 6c 6f 77 60 60 20 77 69 6c 6c 20 62 65 20 72 w``,.values.of.``low``.will.be.r
854a0 65 74 75 72 6e 65 64 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 eturned...........Examples......
854c0 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 ...--------.........Draw.samples
854e0 20 66 72 6f 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 .from.the.distribution:.........
85500 20 3e 3e 3e 20 73 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 .>>>.s.=.np.random.default_rng()
85520 2e 75 6e 69 66 6f 72 6d 28 2d 31 2c 30 2c 31 30 30 30 29 0a 0a 20 20 20 20 20 20 20 20 41 6c 6c .uniform(-1,0,1000)..........All
85540 20 76 61 6c 75 65 73 20 61 72 65 20 77 69 74 68 69 6e 20 74 68 65 20 67 69 76 65 6e 20 69 6e 74 .values.are.within.the.given.int
85560 65 72 76 61 6c 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6e 70 2e 61 6c 6c 28 73 20 3e 3d 20 erval:..........>>>.np.all(s.>=.
85580 2d 31 29 0a 20 20 20 20 20 20 20 20 54 72 75 65 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6e 70 2e -1).........True.........>>>.np.
855a0 61 6c 6c 28 73 20 3c 20 30 29 0a 20 20 20 20 20 20 20 20 54 72 75 65 0a 0a 20 20 20 20 20 20 20 all(s.<.0).........True.........
855c0 20 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 20 6f 66 20 74 68 65 20 73 61 .Display.the.histogram.of.the.sa
855e0 6d 70 6c 65 73 2c 20 61 6c 6f 6e 67 20 77 69 74 68 20 74 68 65 0a 20 20 20 20 20 20 20 20 70 72 mples,.along.with.the.........pr
85600 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 3a 0a 0a 20 20 20 obability.density.function:.....
85620 20 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f .....>>>.import.matplotlib.pyplo
85640 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 63 6f 75 6e 74 2c 20 62 69 6e 73 t.as.plt.........>>>.count,.bins
85660 2c 20 69 67 6e 6f 72 65 64 20 3d 20 70 6c 74 2e 68 69 73 74 28 73 2c 20 31 35 2c 20 64 65 6e 73 ,.ignored.=.plt.hist(s,.15,.dens
85680 69 74 79 3d 54 72 75 65 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 70 6c 6f 74 28 62 ity=True).........>>>.plt.plot(b
856a0 69 6e 73 2c 20 6e 70 2e 6f 6e 65 73 5f 6c 69 6b 65 28 62 69 6e 73 29 2c 20 6c 69 6e 65 77 69 64 ins,.np.ones_like(bins),.linewid
856c0 74 68 3d 32 2c 20 63 6f 6c 6f 72 3d 27 72 27 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 th=2,.color='r').........>>>.plt
856e0 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 20 20 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .show().........................
85700 c8 cb 07 80 01 00 00 00 90 59 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .........Y......................
85720 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
85740 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 b0 d8 01 80 01 00 00 00 00 00 00 00 00 00 00 00 ................................
85760 0a 20 20 20 20 20 20 20 20 64 69 72 69 63 68 6c 65 74 28 61 6c 70 68 61 2c 20 73 69 7a 65 3d 4e .........dirichlet(alpha,.size=N
85780 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 one)..........Draw.samples.from.
857a0 74 68 65 20 44 69 72 69 63 68 6c 65 74 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 the.Dirichlet.distribution......
857c0 20 20 20 20 20 44 72 61 77 20 60 73 69 7a 65 60 20 73 61 6d 70 6c 65 73 20 6f 66 20 64 69 6d 65 .....Draw.`size`.samples.of.dime
857e0 6e 73 69 6f 6e 20 6b 20 66 72 6f 6d 20 61 20 44 69 72 69 63 68 6c 65 74 20 64 69 73 74 72 69 62 nsion.k.from.a.Dirichlet.distrib
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85920 20 20 20 20 20 20 20 20 61 6c 70 68 61 20 3a 20 73 65 71 75 65 6e 63 65 20 6f 66 20 66 6c 6f 61 ........alpha.:.sequence.of.floa
85940 74 73 2c 20 6c 65 6e 67 74 68 20 6b 0a 20 20 20 20 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 ts,.length.k.............Paramet
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85980 60 6b 60 60 20 66 6f 72 20 73 61 6d 70 6c 65 20 6f 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 6c `k``.for.sample.of.............l
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859e0 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 ........Output.shape...If.the.gi
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85a20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 then.............``m.*.n.*.k``.s
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85a60 6e 65 2c 20 69 6e 20 77 68 69 63 68 20 63 61 73 65 20 61 0a 20 20 20 20 20 20 20 20 20 20 20 20 ne,.in.which.case.a.............
85a80 76 65 63 74 6f 72 20 6f 66 20 6c 65 6e 67 74 68 20 60 60 6b 60 60 20 69 73 20 72 65 74 75 72 6e vector.of.length.``k``.is.return
85aa0 65 64 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d ed...........Returns.........---
85ac0 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 61 6d 70 6c 65 73 20 3a 20 6e 64 61 72 72 61 79 2c 0a ----.........samples.:.ndarray,.
85ae0 20 20 20 20 20 20 20 20 20 20 20 20 54 68 65 20 64 72 61 77 6e 20 73 61 6d 70 6c 65 73 2c 20 6f ............The.drawn.samples,.o
85b00 66 20 73 68 61 70 65 20 60 60 28 73 69 7a 65 2c 20 6b 29 60 60 2e 0a 0a 20 20 20 20 20 20 20 20 f.shape.``(size,.k)``...........
85b20 52 61 69 73 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 56 61 Raises.........------.........Va
85b40 6c 75 65 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 61 6e 79 20 76 61 6c 75 lueError.............If.any.valu
85b60 65 20 69 6e 20 60 60 61 6c 70 68 61 60 60 20 69 73 20 6c 65 73 73 20 74 68 61 6e 20 6f 72 20 65 e.in.``alpha``.is.less.than.or.e
85b80 71 75 61 6c 20 74 6f 20 7a 65 72 6f 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 qual.to.zero..........Notes.....
85ba0 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 44 69 72 69 63 68 6c 65 74 20 ....-----.........The.Dirichlet.
85bc0 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 20 61 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 6f distribution.is.a.distribution.o
85be0 76 65 72 20 76 65 63 74 6f 72 73 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 78 60 20 74 68 ver.vectors.........:math:`x`.th
85c00 61 74 20 66 75 6c 66 69 6c 20 74 68 65 20 63 6f 6e 64 69 74 69 6f 6e 73 20 3a 6d 61 74 68 3a 60 at.fulfil.the.conditions.:math:`
85c20 78 5f 69 3e 30 60 20 61 6e 64 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 5c 73 75 6d 5f 7b x_i>0`.and.........:math:`\sum_{
85c40 69 3d 31 7d 5e 6b 20 78 5f 69 20 3d 20 31 60 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 i=1}^k.x_i.=.1`...........The.pr
85c60 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 20 3a 6d 61 74 68 obability.density.function.:math
85c80 3a 60 70 60 20 6f 66 20 61 0a 20 20 20 20 20 20 20 20 44 69 72 69 63 68 6c 65 74 2d 64 69 73 74 :`p`.of.a.........Dirichlet-dist
85ca0 72 69 62 75 74 65 64 20 72 61 6e 64 6f 6d 20 76 65 63 74 6f 72 20 3a 6d 61 74 68 3a 60 58 60 20 ributed.random.vector.:math:`X`.
85cc0 69 73 0a 20 20 20 20 20 20 20 20 70 72 6f 70 6f 72 74 69 6f 6e 61 6c 20 74 6f 0a 0a 20 20 20 20 is.........proportional.to......
85ce0 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 5c 70 72 6f 70 74 6f 20 5c 70 72 6f 64 .......math::.p(x).\propto.\prod
85d00 5f 7b 69 3d 31 7d 5e 7b 6b 7d 7b 78 5e 7b 5c 61 6c 70 68 61 5f 69 2d 31 7d 5f 69 7d 2c 0a 0a 20 _{i=1}^{k}{x^{\alpha_i-1}_i},...
85d20 20 20 20 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 5c 61 6c 70 68 61 60 20 69 73 20 61 .......where.:math:`\alpha`.is.a
85d40 20 76 65 63 74 6f 72 20 63 6f 6e 74 61 69 6e 69 6e 67 20 74 68 65 20 70 6f 73 69 74 69 76 65 0a .vector.containing.the.positive.
85d60 20 20 20 20 20 20 20 20 63 6f 6e 63 65 6e 74 72 61 74 69 6f 6e 20 70 61 72 61 6d 65 74 65 72 73 ........concentration.parameters
85d80 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 6d 65 74 68 6f 64 20 75 73 65 73 20 74 68 65 20 66 ...........The.method.uses.the.f
85da0 6f 6c 6c 6f 77 69 6e 67 20 70 72 6f 70 65 72 74 79 20 66 6f 72 20 63 6f 6d 70 75 74 61 74 69 6f ollowing.property.for.computatio
85dc0 6e 3a 20 6c 65 74 20 3a 6d 61 74 68 3a 60 59 60 0a 20 20 20 20 20 20 20 20 62 65 20 61 20 72 61 n:.let.:math:`Y`.........be.a.ra
85de0 6e 64 6f 6d 20 76 65 63 74 6f 72 20 77 68 69 63 68 20 68 61 73 20 63 6f 6d 70 6f 6e 65 6e 74 73 ndom.vector.which.has.components
85e00 20 74 68 61 74 20 66 6f 6c 6c 6f 77 20 61 20 73 74 61 6e 64 61 72 64 20 67 61 6d 6d 61 0a 20 20 .that.follow.a.standard.gamma...
85e20 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 20 74 68 65 6e 20 3a 6d 61 74 68 3a 60 ......distribution,.then.:math:`
85e40 58 20 3d 20 5c 66 72 61 63 7b 31 7d 7b 5c 73 75 6d 5f 7b 69 3d 31 7d 5e 6b 7b 59 5f 69 7d 7d 20 X.=.\frac{1}{\sum_{i=1}^k{Y_i}}.
85e60 59 60 0a 20 20 20 20 20 20 20 20 69 73 20 44 69 72 69 63 68 6c 65 74 2d 64 69 73 74 72 69 62 75 Y`.........is.Dirichlet-distribu
85e80 74 65 64 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 ted..........References.........
85ea0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 44 61 76 69 64 20 ----------............[1].David.
85ec0 4d 63 4b 61 79 2c 20 22 49 6e 66 6f 72 6d 61 74 69 6f 6e 20 54 68 65 6f 72 79 2c 20 49 6e 66 65 McKay,."Information.Theory,.Infe
85ee0 72 65 6e 63 65 20 61 6e 64 20 4c 65 61 72 6e 69 6e 67 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 rence.and.Learning..............
85f00 20 20 41 6c 67 6f 72 69 74 68 6d 73 2c 22 20 63 68 61 70 74 65 72 20 32 33 2c 0a 20 20 20 20 20 ..Algorithms,".chapter.23,......
85f20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 77 77 77 2e 69 6e 66 65 72 65 6e 63 65 2e 6f ..........http://www.inference.o
85f40 72 67 2e 75 6b 2f 6d 61 63 6b 61 79 2f 69 74 69 6c 61 2f 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b rg.uk/mackay/itila/............[
85f60 32 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 44 69 72 69 63 68 6c 65 74 20 64 69 73 74 72 69 62 2].Wikipedia,."Dirichlet.distrib
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85fa0 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 44 69 72 69 63 68 6c 65 74 5f 64 n.wikipedia.org/wiki/Dirichlet_d
85fc0 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 istribution..........Examples...
85fe0 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 61 6b 69 6e 67 20 61 6e ......--------.........Taking.an
86000 20 65 78 61 6d 70 6c 65 20 63 69 74 65 64 20 69 6e 20 57 69 6b 69 70 65 64 69 61 2c 20 74 68 69 .example.cited.in.Wikipedia,.thi
86020 73 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 63 61 6e 20 62 65 20 75 73 65 64 20 69 66 0a 20 20 s.distribution.can.be.used.if...
86040 20 20 20 20 20 20 6f 6e 65 20 77 61 6e 74 65 64 20 74 6f 20 63 75 74 20 73 74 72 69 6e 67 73 20 ......one.wanted.to.cut.strings.
86060 28 65 61 63 68 20 6f 66 20 69 6e 69 74 69 61 6c 20 6c 65 6e 67 74 68 20 31 2e 30 29 20 69 6e 74 (each.of.initial.length.1.0).int
86080 6f 20 4b 20 70 69 65 63 65 73 0a 20 20 20 20 20 20 20 20 77 69 74 68 20 64 69 66 66 65 72 65 6e o.K.pieces.........with.differen
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860e0 20 20 61 76 65 72 61 67 65 20 6c 65 6e 67 74 68 2c 20 62 75 74 20 61 6c 6c 6f 77 69 6e 67 20 73 ..average.length,.but.allowing.s
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86140 20 20 20 20 3e 3e 3e 20 73 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e ....>>>.s.=.np.random.default_rn
86160 67 28 29 2e 64 69 72 69 63 68 6c 65 74 28 28 31 30 2c 20 35 2c 20 33 29 2c 20 32 30 29 2e 74 72 g().dirichlet((10,.5,.3),.20).tr
86180 61 6e 73 70 6f 73 65 28 29 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 6d 61 anspose()..........>>>.import.ma
861a0 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e tplotlib.pyplot.as.plt.........>
861c0 3e 3e 20 70 6c 74 2e 62 61 72 68 28 72 61 6e 67 65 28 32 30 29 2c 20 73 5b 30 5d 29 0a 20 20 20 >>.plt.barh(range(20),.s[0])....
861e0 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 62 61 72 68 28 72 61 6e 67 65 28 32 30 29 2c 20 73 5b 31 .....>>>.plt.barh(range(20),.s[1
86200 5d 2c 20 6c 65 66 74 3d 73 5b 30 5d 2c 20 63 6f 6c 6f 72 3d 27 67 27 29 0a 20 20 20 20 20 20 20 ],.left=s[0],.color='g')........
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86280 6e 67 73 22 29 0a 0a 20 20 20 20 20 20 20 20 00 0a 20 20 20 20 20 20 20 20 77 61 6c 64 28 6d 65 ngs")....................wald(me
862a0 61 6e 2c 20 73 63 61 6c 65 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 an,.scale,.size=None)..........D
862c0 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 57 61 6c 64 2c 20 6f 72 20 69 6e 76 65 raw.samples.from.a.Wald,.or.inve
862e0 72 73 65 20 47 61 75 73 73 69 61 6e 2c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 rse.Gaussian,.distribution......
86300 20 20 20 20 20 41 73 20 74 68 65 20 73 63 61 6c 65 20 61 70 70 72 6f 61 63 68 65 73 20 69 6e 66 .....As.the.scale.approaches.inf
86320 69 6e 69 74 79 2c 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 62 65 63 6f 6d 65 73 20 inity,.the.distribution.becomes.
86340 6d 6f 72 65 20 6c 69 6b 65 20 61 0a 20 20 20 20 20 20 20 20 47 61 75 73 73 69 61 6e 2e 20 53 6f more.like.a.........Gaussian..So
86360 6d 65 20 72 65 66 65 72 65 6e 63 65 73 20 63 6c 61 69 6d 20 74 68 61 74 20 74 68 65 20 57 61 6c me.references.claim.that.the.Wal
86380 64 20 69 73 20 61 6e 20 69 6e 76 65 72 73 65 20 47 61 75 73 73 69 61 6e 0a 20 20 20 20 20 20 20 d.is.an.inverse.Gaussian........
863a0 20 77 69 74 68 20 6d 65 61 6e 20 65 71 75 61 6c 20 74 6f 20 31 2c 20 62 75 74 20 74 68 69 73 20 .with.mean.equal.to.1,.but.this.
863c0 69 73 20 62 79 20 6e 6f 20 6d 65 61 6e 73 20 75 6e 69 76 65 72 73 61 6c 2e 0a 0a 20 20 20 20 20 is.by.no.means.universal........
863e0 20 20 20 54 68 65 20 69 6e 76 65 72 73 65 20 47 61 75 73 73 69 61 6e 20 64 69 73 74 72 69 62 75 ...The.inverse.Gaussian.distribu
86400 74 69 6f 6e 20 77 61 73 20 66 69 72 73 74 20 73 74 75 64 69 65 64 20 69 6e 20 72 65 6c 61 74 69 tion.was.first.studied.in.relati
86420 6f 6e 73 68 69 70 20 74 6f 0a 20 20 20 20 20 20 20 20 42 72 6f 77 6e 69 61 6e 20 6d 6f 74 69 6f onship.to.........Brownian.motio
86440 6e 2e 20 49 6e 20 31 39 35 36 20 4d 2e 43 2e 4b 2e 20 54 77 65 65 64 69 65 20 75 73 65 64 20 74 n..In.1956.M.C.K..Tweedie.used.t
86460 68 65 20 6e 61 6d 65 20 69 6e 76 65 72 73 65 20 47 61 75 73 73 69 61 6e 0a 20 20 20 20 20 20 20 he.name.inverse.Gaussian........
86480 20 62 65 63 61 75 73 65 20 74 68 65 72 65 20 69 73 20 61 6e 20 69 6e 76 65 72 73 65 20 72 65 6c .because.there.is.an.inverse.rel
864a0 61 74 69 6f 6e 73 68 69 70 20 62 65 74 77 65 65 6e 20 74 68 65 20 74 69 6d 65 20 74 6f 20 63 6f ationship.between.the.time.to.co
864c0 76 65 72 20 61 0a 20 20 20 20 20 20 20 20 75 6e 69 74 20 64 69 73 74 61 6e 63 65 20 61 6e 64 20 ver.a.........unit.distance.and.
864e0 64 69 73 74 61 6e 63 65 20 63 6f 76 65 72 65 64 20 69 6e 20 75 6e 69 74 20 74 69 6d 65 2e 0a 0a distance.covered.in.unit.time...
86500 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d ........Parameters.........-----
86520 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6d 65 61 6e 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 -----.........mean.:.float.or.ar
86540 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 ray_like.of.floats.............D
86560 69 73 74 72 69 62 75 74 69 6f 6e 20 6d 65 61 6e 2c 20 6d 75 73 74 20 62 65 20 3e 20 30 2e 0a 20 istribution.mean,.must.be.>.0...
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86600 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 onal.............Output.shape...
86620 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 If.the.given.shape.is,.e.g.,.``(
86640 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d m,.n,.k)``,.then.............``m
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866a0 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 ..........a.single.value.is.retu
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866e0 72 65 20 62 6f 74 68 20 73 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 68 re.both.scalars..............Oth
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86740 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 .......Returns.........-------..
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867e0 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 ........The.probability.density.
86800 66 75 6e 63 74 69 6f 6e 20 66 6f 72 20 74 68 65 20 57 61 6c 64 20 64 69 73 74 72 69 62 75 74 69 function.for.the.Wald.distributi
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86880 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5c 66 72 61 63 7b 2d 73 63 61 6c 65 28 78 2d 6d 65 ...............\frac{-scale(x-me
868a0 61 6e 29 5e 32 7d 7b 32 5c 63 64 6f 74 70 20 6d 65 61 6e 5e 32 78 7d 0a 0a 20 20 20 20 20 20 20 an)^2}{2\cdotp.mean^2x}.........
868c0 20 41 73 20 6e 6f 74 65 64 20 61 62 6f 76 65 20 74 68 65 20 69 6e 76 65 72 73 65 20 47 61 75 73 .As.noted.above.the.inverse.Gaus
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869c0 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d ......References.........-------
869e0 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 42 72 69 67 68 74 6f 6e 20 57 65 62 73 ---............[1].Brighton.Webs
86a00 20 4c 74 64 2e 2c 20 57 61 6c 64 20 44 69 73 74 72 69 62 75 74 69 6f 6e 2c 0a 20 20 20 20 20 20 .Ltd.,.Wald.Distribution,.......
86a20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 77 65 62 2e 61 72 63 68 69 76 65 2e 6f 72 67 .........https://web.archive.org
86a40 2f 77 65 62 2f 32 30 30 39 30 34 32 33 30 31 34 30 31 30 2f 68 74 74 70 3a 2f 2f 77 77 77 2e 62 /web/20090423014010/http://www.b
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86a80 6f 6e 73 2f 77 61 6c 64 2e 61 73 70 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 43 68 68 69 ons/wald.asp............[2].Chhi
86aa0 6b 61 72 61 2c 20 52 61 6a 20 53 2e 2c 20 61 6e 64 20 46 6f 6c 6b 73 2c 20 4a 2e 20 4c 65 72 6f kara,.Raj.S.,.and.Folks,.J..Lero
86ac0 79 2c 20 22 54 68 65 20 49 6e 76 65 72 73 65 20 47 61 75 73 73 69 61 6e 0a 20 20 20 20 20 20 20 y,."The.Inverse.Gaussian........
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86b40 20 20 20 20 20 20 20 2e 2e 20 5b 33 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 49 6e 76 65 72 73 ..........[3].Wikipedia,."Invers
86b60 65 20 47 61 75 73 73 69 61 6e 20 64 69 73 74 72 69 62 75 74 69 6f 6e 22 0a 20 20 20 20 20 20 20 e.Gaussian.distribution"........
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86ba0 2f 77 69 6b 69 2f 49 6e 76 65 72 73 65 5f 47 61 75 73 73 69 61 6e 5f 64 69 73 74 72 69 62 75 74 /wiki/Inverse_Gaussian_distribut
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8b840 20 4a 6f 68 6e 73 6f 6e 2c 20 4f 6e 20 74 68 65 20 50 61 72 65 74 6f 20 44 69 73 74 72 69 62 75 .Johnson,.On.the.Pareto.Distribu
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8bb00 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a import.matplotlib.pyplot.as.plt.
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8bc80 20 6c 6f 63 61 74 69 6f 6e 20 28 6f 72 20 6d 65 61 6e 29 20 61 6e 64 20 73 63 61 6c 65 20 28 64 .location.(or.mean).and.scale.(d
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8c260 6d 61 67 6e 69 74 75 64 65 20 6f 66 20 74 68 65 20 65 72 72 6f 72 2c 20 77 68 69 63 68 20 6c 65 magnitude.of.the.error,.which.le
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8c380 61 6d 6f 77 69 74 7a 2c 20 4d 2e 20 61 6e 64 20 53 74 65 67 75 6e 2c 20 49 2e 20 41 2e 20 28 45 amowitz,.M..and.Stegun,.I..A..(E
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8c3c0 20 20 4d 61 74 68 65 6d 61 74 69 63 61 6c 20 46 75 6e 63 74 69 6f 6e 73 20 77 69 74 68 20 46 6f ..Mathematical.Functions.with.Fo
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8c400 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 54 61 62 6c 65 73 2c 20 39 74 68 20 70 72 69 6e ................Tables,.9th.prin
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8c480 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 6c 69 7a 61 74 69 6f 6e 73 2c ................Generalizations,
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8c4c0 5b 33 5d 20 57 65 69 73 73 74 65 69 6e 2c 20 45 72 69 63 20 57 2e 20 22 4c 61 70 6c 61 63 65 20 [3].Weisstein,.Eric.W.."Laplace.
8c4e0 44 69 73 74 72 69 62 75 74 69 6f 6e 2e 22 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 46 72 Distribution."................Fr
8c500 6f 6d 20 4d 61 74 68 57 6f 72 6c 64 2d 2d 41 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 65 73 6f om.MathWorld--A.Wolfram.Web.Reso
8c520 75 72 63 65 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d 61 74 68 urce.................http://math
8c540 77 6f 72 6c 64 2e 77 6f 6c 66 72 61 6d 2e 63 6f 6d 2f 4c 61 70 6c 61 63 65 44 69 73 74 72 69 62 world.wolfram.com/LaplaceDistrib
8c560 75 74 69 6f 6e 2e 68 74 6d 6c 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 34 5d 20 57 69 6b 69 70 65 ution.html............[4].Wikipe
8c580 64 69 61 2c 20 22 4c 61 70 6c 61 63 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 22 2c 0a 20 20 20 dia,."Laplace.distribution",....
8c5a0 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 ............https://en.wikipedia
8c5c0 2e 6f 72 67 2f 77 69 6b 69 2f 4c 61 70 6c 61 63 65 5f 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a .org/wiki/Laplace_distribution..
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8c700 20 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 .import.matplotlib.pyplot.as.plt
8c720 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 63 6f 75 6e 74 2c 20 62 69 6e 73 2c 20 69 67 6e 6f 72 65 .........>>>.count,.bins,.ignore
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8c7e0 20 20 20 20 20 20 20 50 6c 6f 74 20 47 61 75 73 73 69 61 6e 20 66 6f 72 20 63 6f 6d 70 61 72 69 .......Plot.Gaussian.for.compari
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8c820 2a 20 6e 70 2e 73 71 72 74 28 32 20 2a 20 6e 70 2e 70 69 29 29 20 2a 0a 20 20 20 20 20 20 20 20 *.np.sqrt(2.*.np.pi)).*.........
8c840 2e 2e 2e 20 20 20 20 20 20 6e 70 2e 65 78 70 28 2d 28 78 20 2d 20 6c 6f 63 29 2a 2a 32 20 2f 20 .........np.exp(-(x.-.loc)**2./.
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8c880 2e 70 6c 6f 74 28 78 2c 67 29 0a 0a 20 20 20 20 20 20 20 20 00 00 00 00 00 00 00 00 00 00 00 00 .plot(x,g)......................
8c8a0 43 6f 6e 73 74 72 75 63 74 20 61 20 6e 65 77 20 47 65 6e 65 72 61 74 6f 72 20 77 69 74 68 20 74 Construct.a.new.Generator.with.t
8c8c0 68 65 20 64 65 66 61 75 6c 74 20 42 69 74 47 65 6e 65 72 61 74 6f 72 20 28 50 43 47 36 34 29 2e he.default.BitGenerator.(PCG64).
8c8e0 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a ......Parameters.....----------.
8c900 20 20 20 20 73 65 65 64 20 3a 20 7b 4e 6f 6e 65 2c 20 69 6e 74 2c 20 61 72 72 61 79 5f 6c 69 6b ....seed.:.{None,.int,.array_lik
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8c9c0 6c 6c 20 62 65 20 70 75 6c 6c 65 64 20 66 72 6f 6d 20 74 68 65 20 4f 53 2e 20 49 66 20 61 6e 20 ll.be.pulled.from.the.OS..If.an.
8c9e0 60 60 69 6e 74 60 60 20 6f 72 0a 20 20 20 20 20 20 20 20 60 60 61 72 72 61 79 5f 6c 69 6b 65 5b ``int``.or.........``array_like[
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8caa0 73 74 61 6e 63 65 2e 0a 20 20 20 20 20 20 20 20 41 64 64 69 74 69 6f 6e 61 6c 6c 79 2c 20 77 68 stance..........Additionally,.wh
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8cb40 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 65 6e 65 ....Returns.....-------.....Gene
8cb60 72 61 74 6f 72 0a 20 20 20 20 20 20 20 20 54 68 65 20 69 6e 69 74 69 61 6c 69 7a 65 64 20 67 65 rator.........The.initialized.ge
8cb80 6e 65 72 61 74 6f 72 20 6f 62 6a 65 63 74 2e 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d nerator.object.......Notes.....-
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8cbc0 69 74 47 65 6e 65 72 61 74 6f 72 60 20 6f 72 20 61 20 60 47 65 6e 65 72 61 74 6f 72 60 2c 20 61 itGenerator`.or.a.`Generator`,.a
8cbe0 20 6e 65 77 20 60 42 69 74 47 65 6e 65 72 61 74 6f 72 60 0a 20 20 20 20 69 73 20 69 6e 73 74 61 .new.`BitGenerator`.....is.insta
8cc00 6e 74 69 61 74 65 64 2e 20 54 68 69 73 20 66 75 6e 63 74 69 6f 6e 20 64 6f 65 73 20 6e 6f 74 20 ntiated..This.function.does.not.
8cc20 6d 61 6e 61 67 65 20 61 20 64 65 66 61 75 6c 74 20 67 6c 6f 62 61 6c 20 69 6e 73 74 61 6e 63 65 manage.a.default.global.instance
8cc40 2e 0a 20 20 20 20 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d ...........Examples.....--------
8cc60 0a 20 20 20 20 60 60 64 65 66 61 75 6c 74 5f 72 6e 67 60 60 20 69 73 20 74 68 65 20 72 65 63 6f .....``default_rng``.is.the.reco
8cc80 6d 6d 65 6e 64 65 64 20 63 6f 6e 73 74 72 75 63 74 6f 72 20 66 6f 72 20 74 68 65 20 72 61 6e 64 mmended.constructor.for.the.rand
8cca0 6f 6d 20 6e 75 6d 62 65 72 20 63 6c 61 73 73 0a 20 20 20 20 60 60 47 65 6e 65 72 61 74 6f 72 60 om.number.class.....``Generator`
8ccc0 60 2e 20 48 65 72 65 20 61 72 65 20 73 65 76 65 72 61 6c 20 77 61 79 73 20 77 65 20 63 61 6e 20 `..Here.are.several.ways.we.can.
8cce0 63 6f 6e 73 74 72 75 63 74 20 61 20 72 61 6e 64 6f 6d 20 0a 20 20 20 20 6e 75 6d 62 65 72 20 67 construct.a.random......number.g
8cd00 65 6e 65 72 61 74 6f 72 20 75 73 69 6e 67 20 60 60 64 65 66 61 75 6c 74 5f 72 6e 67 60 60 20 61 enerator.using.``default_rng``.a
8cd20 6e 64 20 74 68 65 20 60 60 47 65 6e 65 72 61 74 6f 72 60 60 20 63 6c 61 73 73 2e 20 0a 20 20 20 nd.the.``Generator``.class......
8cd40 20 0a 20 20 20 20 48 65 72 65 20 77 65 20 75 73 65 20 60 60 64 65 66 61 75 6c 74 5f 72 6e 67 60 ......Here.we.use.``default_rng`
8cd60 60 20 74 6f 20 67 65 6e 65 72 61 74 65 20 61 20 72 61 6e 64 6f 6d 20 66 6c 6f 61 74 3a 0a 20 0a `.to.generate.a.random.float:...
8cd80 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 6e 75 6d 70 79 20 61 73 20 6e 70 0a 20 20 20 20 3e ....>>>.import.numpy.as.np.....>
8cda0 3e 3e 20 72 6e 67 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 31 >>.rng.=.np.random.default_rng(1
8cdc0 32 33 34 35 29 0a 20 20 20 20 3e 3e 3e 20 70 72 69 6e 74 28 72 6e 67 29 0a 20 20 20 20 47 65 6e 2345).....>>>.print(rng).....Gen
8cde0 65 72 61 74 6f 72 28 50 43 47 36 34 29 0a 20 20 20 20 3e 3e 3e 20 72 66 6c 6f 61 74 20 3d 20 72 erator(PCG64).....>>>.rfloat.=.r
8ce00 6e 67 2e 72 61 6e 64 6f 6d 28 29 0a 20 20 20 20 3e 3e 3e 20 72 66 6c 6f 61 74 0a 20 20 20 20 30 ng.random().....>>>.rfloat.....0
8ce20 2e 32 32 37 33 33 36 30 32 32 34 36 37 31 36 39 36 36 0a 20 20 20 20 3e 3e 3e 20 74 79 70 65 28 .22733602246716966.....>>>.type(
8ce40 72 66 6c 6f 61 74 29 0a 20 20 20 20 3c 63 6c 61 73 73 20 27 66 6c 6f 61 74 27 3e 0a 20 20 20 20 rfloat).....<class.'float'>.....
8ce60 20 0a 20 20 20 20 48 65 72 65 20 77 65 20 75 73 65 20 60 60 64 65 66 61 75 6c 74 5f 72 6e 67 60 ......Here.we.use.``default_rng`
8ce80 60 20 74 6f 20 67 65 6e 65 72 61 74 65 20 33 20 72 61 6e 64 6f 6d 20 69 6e 74 65 67 65 72 73 20 `.to.generate.3.random.integers.
8cea0 62 65 74 77 65 65 6e 20 30 20 0a 20 20 20 20 28 69 6e 63 6c 75 73 69 76 65 29 20 61 6e 64 20 31 between.0......(inclusive).and.1
8cec0 30 20 28 65 78 63 6c 75 73 69 76 65 29 3a 0a 20 20 20 20 20 20 20 20 0a 20 20 20 20 3e 3e 3e 20 0.(exclusive):..............>>>.
8cee0 69 6d 70 6f 72 74 20 6e 75 6d 70 79 20 61 73 20 6e 70 0a 20 20 20 20 3e 3e 3e 20 72 6e 67 20 3d import.numpy.as.np.....>>>.rng.=
8cf00 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 31 32 33 34 35 29 0a 20 20 .np.random.default_rng(12345)...
8cf20 20 20 3e 3e 3e 20 72 69 6e 74 73 20 3d 20 72 6e 67 2e 69 6e 74 65 67 65 72 73 28 6c 6f 77 3d 30 ..>>>.rints.=.rng.integers(low=0
8cf40 2c 20 68 69 67 68 3d 31 30 2c 20 73 69 7a 65 3d 33 29 0a 20 20 20 20 3e 3e 3e 20 72 69 6e 74 73 ,.high=10,.size=3).....>>>.rints
8cf60 0a 20 20 20 20 61 72 72 61 79 28 5b 36 2c 20 32 2c 20 37 5d 29 0a 20 20 20 20 3e 3e 3e 20 74 79 .....array([6,.2,.7]).....>>>.ty
8cf80 70 65 28 72 69 6e 74 73 5b 30 5d 29 0a 20 20 20 20 3c 63 6c 61 73 73 20 27 6e 75 6d 70 79 2e 69 pe(rints[0]).....<class.'numpy.i
8cfa0 6e 74 36 34 27 3e 0a 20 20 20 20 0a 20 20 20 20 48 65 72 65 20 77 65 20 73 70 65 63 69 66 79 20 nt64'>..........Here.we.specify.
8cfc0 61 20 73 65 65 64 20 73 6f 20 74 68 61 74 20 77 65 20 68 61 76 65 20 72 65 70 72 6f 64 75 63 69 a.seed.so.that.we.have.reproduci
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8d000 20 6e 75 6d 70 79 20 61 73 20 6e 70 0a 20 20 20 20 3e 3e 3e 20 72 6e 67 20 3d 20 6e 70 2e 72 61 .numpy.as.np.....>>>.rng.=.np.ra
8d020 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 73 65 65 64 3d 34 32 29 0a 20 20 20 20 3e 3e ndom.default_rng(seed=42).....>>
8d040 3e 20 70 72 69 6e 74 28 72 6e 67 29 0a 20 20 20 20 47 65 6e 65 72 61 74 6f 72 28 50 43 47 36 34 >.print(rng).....Generator(PCG64
8d060 29 0a 20 20 20 20 3e 3e 3e 20 61 72 72 31 20 3d 20 72 6e 67 2e 72 61 6e 64 6f 6d 28 28 33 2c 20 ).....>>>.arr1.=.rng.random((3,.
8d080 33 29 29 0a 20 20 20 20 3e 3e 3e 20 61 72 72 31 0a 20 20 20 20 61 72 72 61 79 28 5b 5b 30 2e 37 3)).....>>>.arr1.....array([[0.7
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8d0c0 2c 0a 20 20 20 20 20 20 20 20 20 20 20 5b 30 2e 36 39 37 33 36 38 30 33 2c 20 30 2e 30 39 34 31 ,............[0.69736803,.0.0941
8d0e0 37 37 33 35 2c 20 30 2e 39 37 35 36 32 32 33 35 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 5b 30 7735,.0.97562235],............[0
8d100 2e 37 36 31 31 33 39 37 20 2c 20 30 2e 37 38 36 30 36 34 33 31 2c 20 30 2e 31 32 38 31 31 33 36 .7611397.,.0.78606431,.0.1281136
8d120 33 5d 5d 29 0a 0a 20 20 20 20 49 66 20 77 65 20 65 78 69 74 20 61 6e 64 20 72 65 73 74 61 72 74 3]])......If.we.exit.and.restart
8d140 20 6f 75 72 20 50 79 74 68 6f 6e 20 69 6e 74 65 72 70 72 65 74 65 72 2c 20 77 65 27 6c 6c 20 73 .our.Python.interpreter,.we'll.s
8d160 65 65 20 74 68 61 74 20 77 65 0a 20 20 20 20 67 65 6e 65 72 61 74 65 20 74 68 65 20 73 61 6d 65 ee.that.we.....generate.the.same
8d180 20 72 61 6e 64 6f 6d 20 6e 75 6d 62 65 72 73 20 61 67 61 69 6e 3a 0a 0a 20 20 20 20 3e 3e 3e 20 .random.numbers.again:......>>>.
8d1a0 69 6d 70 6f 72 74 20 6e 75 6d 70 79 20 61 73 20 6e 70 0a 20 20 20 20 3e 3e 3e 20 72 6e 67 20 3d import.numpy.as.np.....>>>.rng.=
8d1c0 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 73 65 65 64 3d 34 32 29 0a .np.random.default_rng(seed=42).
8d1e0 20 20 20 20 3e 3e 3e 20 61 72 72 32 20 3d 20 72 6e 67 2e 72 61 6e 64 6f 6d 28 28 33 2c 20 33 29 ....>>>.arr2.=.rng.random((3,.3)
8d200 29 0a 20 20 20 20 3e 3e 3e 20 61 72 72 32 0a 20 20 20 20 61 72 72 61 79 28 5b 5b 30 2e 37 37 33 ).....>>>.arr2.....array([[0.773
8d220 39 35 36 30 35 2c 20 30 2e 34 33 38 38 37 38 34 34 2c 20 30 2e 38 35 38 35 39 37 39 32 5d 2c 0a 95605,.0.43887844,.0.85859792],.
8d240 20 20 20 20 20 20 20 20 20 20 20 5b 30 2e 36 39 37 33 36 38 30 33 2c 20 30 2e 30 39 34 31 37 37 ...........[0.69736803,.0.094177
8d260 33 35 2c 20 30 2e 39 37 35 36 32 32 33 35 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 5b 30 2e 37 35,.0.97562235],............[0.7
8d280 36 31 31 33 39 37 20 2c 20 30 2e 37 38 36 30 36 34 33 31 2c 20 30 2e 31 32 38 31 31 33 36 33 5d 611397.,.0.78606431,.0.12811363]
8d2a0 5d 29 0a 0a 20 20 20 20 00 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 72 61 79 6c 65 69 67 ]).......................rayleig
8d2c0 68 28 73 63 61 6c 65 3d 31 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 h(scale=1.0,.size=None).........
8d2e0 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 52 61 79 6c 65 69 67 68 20 64 69 .Draw.samples.from.a.Rayleigh.di
8d300 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 3a 6d 61 74 68 3a 60 stribution...........The.:math:`
8d320 5c 63 68 69 60 20 61 6e 64 20 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 73 20 \chi`.and.Weibull.distributions.
8d340 61 72 65 20 67 65 6e 65 72 61 6c 69 7a 61 74 69 6f 6e 73 20 6f 66 20 74 68 65 0a 20 20 20 20 20 are.generalizations.of.the......
8d360 20 20 20 52 61 79 6c 65 69 67 68 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 ...Rayleigh...........Parameters
8d380 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 61 6c .........----------.........scal
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8d3c0 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 53 63 61 6c 65 2c 20 61 s,.optional.............Scale,.a
8d3e0 6c 73 6f 20 65 71 75 61 6c 73 20 74 68 65 20 6d 6f 64 65 2e 20 4d 75 73 74 20 62 65 20 6e 6f 6e lso.equals.the.mode..Must.be.non
8d400 2d 6e 65 67 61 74 69 76 65 2e 20 44 65 66 61 75 6c 74 20 69 73 20 31 2e 0a 20 20 20 20 20 20 20 -negative..Default.is.1.........
8d420 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 .size.:.int.or.tuple.of.ints,.op
8d440 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e tional.............Output.shape.
8d460 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 ..If.the.given.shape.is,.e.g.,.`
8d480 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 `(m,.n,.k)``,.then.............`
8d4a0 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 `m.*.n.*.k``.samples.are.drawn..
8d4c0 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a .If.size.is.``None``.(default),.
8d4e0 20 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 ............a.single.value.is.re
8d500 74 75 72 6e 65 64 20 69 66 20 60 60 73 63 61 6c 65 60 60 20 69 73 20 61 20 73 63 61 6c 61 72 2e turned.if.``scale``.is.a.scalar.
8d520 20 20 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6e 70 2e 61 72 ..Otherwise,.............``np.ar
8d540 72 61 79 28 73 63 61 6c 65 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 ray(scale).size``.samples.are.dr
8d560 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d awn...........Returns.........--
8d580 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 -----.........out.:.ndarray.or.s
8d5a0 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 calar.............Drawn.samples.
8d5c0 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 52 61 79 6c 65 69 67 68 20 from.the.parameterized.Rayleigh.
8d5e0 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 distribution...........Notes....
8d600 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 .....-----.........The.probabili
8d620 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 20 66 6f 72 20 74 68 65 20 52 61 79 6c ty.density.function.for.the.Rayl
8d640 65 69 67 68 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e eigh.distribution.is............
8d660 20 6d 61 74 68 3a 3a 20 50 28 78 3b 73 63 61 6c 65 29 20 3d 20 5c 66 72 61 63 7b 78 7d 7b 73 63 .math::.P(x;scale).=.\frac{x}{sc
8d680 61 6c 65 5e 32 7d 65 5e 7b 5c 66 72 61 63 7b 2d 78 5e 32 7d 7b 32 20 5c 63 64 6f 74 70 20 73 63 ale^2}e^{\frac{-x^2}{2.\cdotp.sc
8d6a0 61 6c 65 5e 32 7d 7d 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 52 61 79 6c 65 69 67 68 20 64 69 ale^2}}..........The.Rayleigh.di
8d6c0 73 74 72 69 62 75 74 69 6f 6e 20 77 6f 75 6c 64 20 61 72 69 73 65 2c 20 66 6f 72 20 65 78 61 6d stribution.would.arise,.for.exam
8d6e0 70 6c 65 2c 20 69 66 20 74 68 65 20 45 61 73 74 0a 20 20 20 20 20 20 20 20 61 6e 64 20 4e 6f 72 ple,.if.the.East.........and.Nor
8d700 74 68 20 63 6f 6d 70 6f 6e 65 6e 74 73 20 6f 66 20 74 68 65 20 77 69 6e 64 20 76 65 6c 6f 63 69 th.components.of.the.wind.veloci
8d720 74 79 20 68 61 64 20 69 64 65 6e 74 69 63 61 6c 20 7a 65 72 6f 2d 6d 65 61 6e 0a 20 20 20 20 20 ty.had.identical.zero-mean......
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90ce0 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 61 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 ---------.........a.:.float.or.a
90d00 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 rray_like.of.floats.............
90d20 53 68 61 70 65 20 70 61 72 61 6d 65 74 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 Shape.parameter.of.the.distribut
90d40 69 6f 6e 2e 20 20 4d 75 73 74 20 62 65 20 6e 6f 6e 6e 65 67 61 74 69 76 65 2e 0a 20 20 20 20 20 ion...Must.be.nonnegative.......
90d60 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 ...size.:.int.or.tuple.of.ints,.
90d80 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 optional.............Output.shap
90da0 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c e...If.the.given.shape.is,.e.g.,
90dc0 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 .``(m,.n,.k)``,.then............
90de0 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e .``m.*.n.*.k``.samples.are.drawn
90e00 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 ...If.size.is.``None``.(default)
90e20 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 ,.............a.single.value.is.
90e40 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 61 60 60 20 69 73 20 61 20 73 63 61 6c 61 72 2e 20 20 returned.if.``a``.is.a.scalar...
90e60 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6e 70 2e 61 72 72 61 Otherwise,.............``np.arra
90e80 79 28 61 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a y(a).size``.samples.are.drawn...
90ea0 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a ........Returns.........-------.
90ec0 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a ........out.:.ndarray.or.scalar.
90ee0 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 ............Drawn.samples.from.t
90f00 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 he.parameterized.Weibull.distrib
90f20 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 ution...........See.Also........
90f40 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 77 65 .--------.........scipy.stats.we
90f60 69 62 75 6c 6c 5f 6d 61 78 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 77 65 ibull_max.........scipy.stats.we
90f80 69 62 75 6c 6c 5f 6d 69 6e 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 67 65 ibull_min.........scipy.stats.ge
90fa0 6e 65 78 74 72 65 6d 65 0a 20 20 20 20 20 20 20 20 67 75 6d 62 65 6c 0a 0a 20 20 20 20 20 20 20 nextreme.........gumbel.........
90fc0 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 .Notes.........-----.........The
90fe0 20 57 65 69 62 75 6c 6c 20 28 6f 72 20 54 79 70 65 20 49 49 49 20 61 73 79 6d 70 74 6f 74 69 63 .Weibull.(or.Type.III.asymptotic
91000 20 65 78 74 72 65 6d 65 20 76 61 6c 75 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 20 20 20 20 .extreme.value.distribution.....
91020 20 20 20 20 66 6f 72 20 73 6d 61 6c 6c 65 73 74 20 76 61 6c 75 65 73 2c 20 53 45 56 20 54 79 70 ....for.smallest.values,.SEV.Typ
91040 65 20 49 49 49 2c 20 6f 72 20 52 6f 73 69 6e 2d 52 61 6d 6d 6c 65 72 0a 20 20 20 20 20 20 20 20 e.III,.or.Rosin-Rammler.........
91060 64 69 73 74 72 69 62 75 74 69 6f 6e 29 20 69 73 20 6f 6e 65 20 6f 66 20 61 20 63 6c 61 73 73 20 distribution).is.one.of.a.class.
91080 6f 66 20 47 65 6e 65 72 61 6c 69 7a 65 64 20 45 78 74 72 65 6d 65 20 56 61 6c 75 65 0a 20 20 20 of.Generalized.Extreme.Value....
910a0 20 20 20 20 20 28 47 45 56 29 20 64 69 73 74 72 69 62 75 74 69 6f 6e 73 20 75 73 65 64 20 69 6e .....(GEV).distributions.used.in
910c0 20 6d 6f 64 65 6c 69 6e 67 20 65 78 74 72 65 6d 65 20 76 61 6c 75 65 20 70 72 6f 62 6c 65 6d 73 .modeling.extreme.value.problems
910e0 2e 0a 20 20 20 20 20 20 20 20 54 68 69 73 20 63 6c 61 73 73 20 69 6e 63 6c 75 64 65 73 20 74 68 ..........This.class.includes.th
91100 65 20 47 75 6d 62 65 6c 20 61 6e 64 20 46 72 65 63 68 65 74 20 64 69 73 74 72 69 62 75 74 69 6f e.Gumbel.and.Frechet.distributio
91120 6e 73 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e ns...........The.probability.den
91140 73 69 74 79 20 66 6f 72 20 74 68 65 20 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 75 74 69 6f sity.for.the.Weibull.distributio
91160 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 5c n.is.............math::.p(x).=.\
91180 66 72 61 63 7b 61 7d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 frac{a}.........................
911a0 20 7b 5c 6c 61 6d 62 64 61 7d 28 5c 66 72 61 63 7b 78 7d 7b 5c 6c 61 6d 62 64 61 7d 29 5e 7b 61 .{\lambda}(\frac{x}{\lambda})^{a
911c0 2d 31 7d 65 5e 7b 2d 28 78 2f 5c 6c 61 6d 62 64 61 29 5e 61 7d 2c 0a 0a 20 20 20 20 20 20 20 20 -1}e^{-(x/\lambda)^a},..........
911e0 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 61 60 20 69 73 20 74 68 65 20 73 68 61 70 65 20 61 6e 64 where.:math:`a`.is.the.shape.and
91200 20 3a 6d 61 74 68 3a 60 5c 6c 61 6d 62 64 61 60 20 74 68 65 20 73 63 61 6c 65 2e 0a 0a 20 20 20 .:math:`\lambda`.the.scale......
91220 20 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 20 68 61 73 20 69 74 73 20 70 65 61 6b 20 28 .....The.function.has.its.peak.(
91240 74 68 65 20 6d 6f 64 65 29 20 61 74 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 5c 6c 61 6d the.mode).at.........:math:`\lam
91260 62 64 61 28 5c 66 72 61 63 7b 61 2d 31 7d 7b 61 7d 29 5e 7b 31 2f 61 7d 60 2e 0a 0a 20 20 20 20 bda(\frac{a-1}{a})^{1/a}`.......
91280 20 20 20 20 57 68 65 6e 20 60 60 61 20 3d 20 31 60 60 2c 20 74 68 65 20 57 65 69 62 75 6c 6c 20 ....When.``a.=.1``,.the.Weibull.
912a0 64 69 73 74 72 69 62 75 74 69 6f 6e 20 72 65 64 75 63 65 73 20 74 6f 20 74 68 65 20 65 78 70 6f distribution.reduces.to.the.expo
912c0 6e 65 6e 74 69 61 6c 0a 20 20 20 20 20 20 20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 nential.........distribution....
912e0 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d .......References.........------
91300 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 57 61 6c 6f 64 64 69 20 57 65 69 62 ----............[1].Waloddi.Weib
91320 75 6c 6c 2c 20 52 6f 79 61 6c 20 54 65 63 68 6e 69 63 61 6c 20 55 6e 69 76 65 72 73 69 74 79 2c ull,.Royal.Technical.University,
91340 20 53 74 6f 63 6b 68 6f 6c 6d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 31 39 33 39 20 .Stockholm,................1939.
91360 22 41 20 53 74 61 74 69 73 74 69 63 61 6c 20 54 68 65 6f 72 79 20 4f 66 20 54 68 65 20 53 74 72 "A.Statistical.Theory.Of.The.Str
91380 65 6e 67 74 68 20 4f 66 20 4d 61 74 65 72 69 61 6c 73 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 ength.Of.Materials",............
913a0 20 20 20 20 49 6e 67 65 6e 69 6f 72 73 76 65 74 65 6e 73 6b 61 70 73 61 6b 61 64 65 6d 69 65 6e ....Ingeniorsvetenskapsakademien
913c0 73 20 48 61 6e 64 6c 69 6e 67 61 72 20 4e 72 20 31 35 31 2c 20 31 39 33 39 2c 0a 20 20 20 20 20 s.Handlingar.Nr.151,.1939,......
913e0 20 20 20 20 20 20 20 20 20 20 47 65 6e 65 72 61 6c 73 74 61 62 65 6e 73 20 4c 69 74 6f 67 72 61 ..........Generalstabens.Litogra
91400 66 69 73 6b 61 20 41 6e 73 74 61 6c 74 73 20 46 6f 72 6c 61 67 2c 20 53 74 6f 63 6b 68 6f 6c 6d fiska.Anstalts.Forlag,.Stockholm
91420 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d 20 57 61 6c 6f 64 64 69 20 57 65 69 62 75 6c 6c .............[2].Waloddi.Weibull
91440 2c 20 22 41 20 53 74 61 74 69 73 74 69 63 61 6c 20 44 69 73 74 72 69 62 75 74 69 6f 6e 20 46 75 ,."A.Statistical.Distribution.Fu
91460 6e 63 74 69 6f 6e 20 6f 66 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 57 69 64 65 20 41 70 nction.of................Wide.Ap
91480 70 6c 69 63 61 62 69 6c 69 74 79 22 2c 20 4a 6f 75 72 6e 61 6c 20 4f 66 20 41 70 70 6c 69 65 64 plicability",.Journal.Of.Applied
914a0 20 4d 65 63 68 61 6e 69 63 73 20 41 53 4d 45 20 50 61 70 65 72 0a 20 20 20 20 20 20 20 20 20 20 .Mechanics.ASME.Paper...........
914c0 20 20 20 20 20 31 39 35 31 2e 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 33 5d 20 57 69 6b 69 70 65 .....1951.............[3].Wikipe
914e0 64 69 61 2c 20 22 57 65 69 62 75 6c 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 22 2c 0a 20 20 20 dia,."Weibull.distribution",....
91500 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 ............https://en.wikipedia
91520 2e 6f 72 67 2f 77 69 6b 69 2f 57 65 69 62 75 6c 6c 5f 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a .org/wiki/Weibull_distribution..
91540 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d ........Examples.........-------
91560 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 -.........Draw.samples.from.the.
91580 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 20 3d distribution:..........>>>.rng.=
915a0 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 20 20 20 20 20 20 .np.random.default_rng()........
915c0 20 3e 3e 3e 20 61 20 3d 20 35 2e 20 23 20 73 68 61 70 65 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 .>>>.a.=.5..#.shape.........>>>.
915e0 73 20 3d 20 72 6e 67 2e 77 65 69 62 75 6c 6c 28 61 2c 20 31 30 30 30 29 0a 0a 20 20 20 20 20 20 s.=.rng.weibull(a,.1000)........
91600 20 20 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 20 6f 66 20 74 68 65 20 73 ..Display.the.histogram.of.the.s
91620 61 6d 70 6c 65 73 2c 20 61 6c 6f 6e 67 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 74 68 65 20 70 amples,.along.with.........the.p
91640 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 3a 0a 0a 20 20 robability.density.function:....
91660 20 20 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c ......>>>.import.matplotlib.pypl
91680 6f 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 78 20 3d 20 6e 70 2e 61 72 61 ot.as.plt.........>>>.x.=.np.ara
916a0 6e 67 65 28 31 2c 31 30 30 2e 29 2f 35 30 2e 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 64 65 66 20 nge(1,100.)/50..........>>>.def.
916c0 77 65 69 62 28 78 2c 6e 2c 61 29 3a 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 72 65 74 weib(x,n,a):.................ret
916e0 75 72 6e 20 28 61 20 2f 20 6e 29 20 2a 20 28 78 20 2f 20 6e 29 2a 2a 28 61 20 2d 20 31 29 20 2a urn.(a./.n).*.(x./.n)**(a.-.1).*
91700 20 6e 70 2e 65 78 70 28 2d 28 78 20 2f 20 6e 29 2a 2a 61 29 0a 0a 20 20 20 20 20 20 20 20 3e 3e .np.exp(-(x./.n)**a)..........>>
91720 3e 20 63 6f 75 6e 74 2c 20 62 69 6e 73 2c 20 69 67 6e 6f 72 65 64 20 3d 20 70 6c 74 2e 68 69 73 >.count,.bins,.ignored.=.plt.his
91740 74 28 72 6e 67 2e 77 65 69 62 75 6c 6c 28 35 2e 2c 31 30 30 30 29 29 0a 20 20 20 20 20 20 20 20 t(rng.weibull(5.,1000)).........
91760 3e 3e 3e 20 78 20 3d 20 6e 70 2e 61 72 61 6e 67 65 28 31 2c 31 30 30 2e 29 2f 35 30 2e 0a 20 20 >>>.x.=.np.arange(1,100.)/50....
91780 20 20 20 20 20 20 3e 3e 3e 20 73 63 61 6c 65 20 3d 20 63 6f 75 6e 74 2e 6d 61 78 28 29 2f 77 65 ......>>>.scale.=.count.max()/we
917a0 69 62 28 78 2c 20 31 2e 2c 20 35 2e 29 2e 6d 61 78 28 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 ib(x,.1.,.5.).max().........>>>.
917c0 70 6c 74 2e 70 6c 6f 74 28 78 2c 20 77 65 69 62 28 78 2c 20 31 2e 2c 20 35 2e 29 2a 73 63 61 6c plt.plot(x,.weib(x,.1.,.5.)*scal
917e0 65 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 e).........>>>.plt.show().......
91800 20 20 20 00 00 00 00 00 00 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 62 79 74 65 73 28 6c .........................bytes(l
91820 65 6e 67 74 68 29 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 20 72 61 6e 64 6f 6d 20 62 79 ength)..........Return.random.by
91840 74 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 tes...........Parameters........
91860 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6c 65 6e 67 74 68 20 3a 20 69 6e 74 .----------.........length.:.int
91880 0a 20 20 20 20 20 20 20 20 20 20 20 20 4e 75 6d 62 65 72 20 6f 66 20 72 61 6e 64 6f 6d 20 62 79 .............Number.of.random.by
918a0 74 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d tes...........Returns.........--
918c0 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 62 79 74 65 73 0a 20 20 20 20 20 20 -----.........out.:.bytes.......
918e0 20 20 20 20 20 20 53 74 72 69 6e 67 20 6f 66 20 6c 65 6e 67 74 68 20 60 6c 65 6e 67 74 68 60 2e ......String.of.length.`length`.
91900 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d ..........Examples.........-----
91920 2d 2d 2d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c ---.........>>>.np.random.defaul
91940 74 5f 72 6e 67 28 29 2e 62 79 74 65 73 28 31 30 29 0a 20 20 20 20 20 20 20 20 62 27 5c 78 66 65 t_rng().bytes(10).........b'\xfe
91960 43 5c 78 39 62 5c 78 38 36 5c 78 31 37 5c 78 66 32 5c 78 61 31 5c 78 61 66 63 70 27 20 23 20 72 C\x9b\x86\x17\xf2\xa1\xafcp'.#.r
91980 61 6e 64 6f 6d 0a 0a 20 20 20 20 20 20 20 20 00 0a 20 20 20 20 20 20 20 20 6e 65 67 61 74 69 76 andom....................negativ
919a0 65 5f 62 69 6e 6f 6d 69 61 6c 28 6e 2c 20 70 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 e_binomial(n,.p,.size=None).....
919c0 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 6e 65 67 61 74 69 76 .....Draw.samples.from.a.negativ
919e0 65 20 62 69 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 e.binomial.distribution.........
91a00 20 20 53 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 20 66 72 6f 6d 20 61 20 6e 65 67 61 74 ..Samples.are.drawn.from.a.negat
91a20 69 76 65 20 62 69 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 77 69 74 68 20 73 ive.binomial.distribution.with.s
91a40 70 65 63 69 66 69 65 64 0a 20 20 20 20 20 20 20 20 70 61 72 61 6d 65 74 65 72 73 2c 20 60 6e 60 pecified.........parameters,.`n`
91a60 20 73 75 63 63 65 73 73 65 73 20 61 6e 64 20 60 70 60 20 70 72 6f 62 61 62 69 6c 69 74 79 20 6f .successes.and.`p`.probability.o
91a80 66 20 73 75 63 63 65 73 73 20 77 68 65 72 65 20 60 6e 60 0a 20 20 20 20 20 20 20 20 69 73 20 3e f.success.where.`n`.........is.>
91aa0 20 30 20 61 6e 64 20 60 70 60 20 69 73 20 69 6e 20 74 68 65 20 69 6e 74 65 72 76 61 6c 20 28 30 .0.and.`p`.is.in.the.interval.(0
91ac0 2c 20 31 5d 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 ,.1]...........Parameters.......
91ae0 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6e 20 3a 20 66 6c 6f 61 74 20 6f ..----------.........n.:.float.o
91b00 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 r.array_like.of.floats..........
91b20 20 20 20 50 61 72 61 6d 65 74 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e ...Parameter.of.the.distribution
91b40 2c 20 3e 20 30 2e 0a 20 20 20 20 20 20 20 20 70 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 ,.>.0..........p.:.float.or.arra
91b60 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 50 61 72 y_like.of.floats.............Par
91b80 61 6d 65 74 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 4d 75 73 74 ameter.of.the.distribution..Must
91ba0 20 73 61 74 69 73 66 79 20 30 20 3c 20 70 20 3c 3d 20 31 2e 0a 20 20 20 20 20 20 20 20 73 69 7a .satisfy.0.<.p.<=.1..........siz
91bc0 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e e.:.int.or.tuple.of.ints,.option
91be0 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 al.............Output.shape...If
91c00 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c .the.given.shape.is,.e.g.,.``(m,
91c20 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a .n,.k)``,.then.............``m.*
91c40 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 20 .n.*.k``.samples.are.drawn...If.
91c60 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 20 size.is.``None``.(default),.....
91c80 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e ........a.single.value.is.return
91ca0 65 64 20 69 66 20 60 60 6e 60 60 20 61 6e 64 20 60 60 70 60 60 20 61 72 65 20 62 6f 74 68 20 73 ed.if.``n``.and.``p``.are.both.s
91cc0 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 74 68 65 72 77 69 73 65 2c 20 60 calars..............Otherwise,.`
91ce0 60 6e 70 2e 62 72 6f 61 64 63 61 73 74 28 6e 2c 20 70 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c `np.broadcast(n,.p).size``.sampl
91d00 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 es.are.drawn...........Returns..
91d20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 .......-------.........out.:.nda
91d40 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e rray.or.scalar.............Drawn
91d60 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 .samples.from.the.parameterized.
91d80 6e 65 67 61 74 69 76 65 20 62 69 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 0a negative.binomial.distribution,.
91da0 20 20 20 20 20 20 20 20 20 20 20 20 77 68 65 72 65 20 65 61 63 68 20 73 61 6d 70 6c 65 20 69 73 ............where.each.sample.is
91dc0 20 65 71 75 61 6c 20 74 6f 20 4e 2c 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 66 61 69 6c 75 .equal.to.N,.the.number.of.failu
91de0 72 65 73 20 74 68 61 74 0a 20 20 20 20 20 20 20 20 20 20 20 20 6f 63 63 75 72 72 65 64 20 62 65 res.that.............occurred.be
91e00 66 6f 72 65 20 61 20 74 6f 74 61 6c 20 6f 66 20 6e 20 73 75 63 63 65 73 73 65 73 20 77 61 73 20 fore.a.total.of.n.successes.was.
91e20 72 65 61 63 68 65 64 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 reached...........Notes.........
91e40 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 6d 61 -----.........The.probability.ma
91e60 73 73 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 74 68 65 20 6e 65 67 61 74 69 76 65 20 62 69 6e 6f ss.function.of.the.negative.bino
91e80 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e mial.distribution.is............
91ea0 20 6d 61 74 68 3a 3a 20 50 28 4e 3b 6e 2c 70 29 20 3d 20 5c 66 72 61 63 7b 5c 47 61 6d 6d 61 28 .math::.P(N;n,p).=.\frac{\Gamma(
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92320 75 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 ution..........Examples.........
92340 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 --------.........Draw.samples.fr
92360 6f 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 41 20 om.the.distribution:..........A.
92380 72 65 61 6c 20 77 6f 72 6c 64 20 65 78 61 6d 70 6c 65 2e 20 41 20 63 6f 6d 70 61 6e 79 20 64 72 real.world.example..A.company.dr
923a0 69 6c 6c 73 20 77 69 6c 64 2d 63 61 74 20 6f 69 6c 0a 20 20 20 20 20 20 20 20 65 78 70 6c 6f 72 ills.wild-cat.oil.........explor
923c0 61 74 69 6f 6e 20 77 65 6c 6c 73 2c 20 65 61 63 68 20 77 69 74 68 20 61 6e 20 65 73 74 69 6d 61 ation.wells,.each.with.an.estima
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924c0 74 63 2e 3f 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e tc.?..........>>>.s.=.np.random.
924e0 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 2e 6e 65 67 61 74 69 76 65 5f 62 69 6e 6f 6d 69 61 6c 28 default_rng().negative_binomial(
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92540 4b 49 50 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 70 72 6f 62 61 62 69 6c 69 74 79 20 3d KIP................probability.=
92560 20 73 75 6d 28 73 3c 69 29 20 2f 20 31 30 30 30 30 30 2e 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 .sum(s<i)./.100000..............
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928c0 0a 20 20 20 20 20 20 20 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 20 20 20 20 49 66 20 .........ndarray.............If.
928e0 60 6f 75 74 60 20 69 73 20 4e 6f 6e 65 2c 20 61 20 73 68 75 66 66 6c 65 64 20 63 6f 70 79 20 6f `out`.is.None,.a.shuffled.copy.o
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92980 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 68 Also.........--------.........sh
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92be0 20 31 31 2c 20 20 38 2c 20 31 33 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 5b 31 37 .11,..8,.13],................[17
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92c20 0a 20 20 20 20 20 20 20 20 60 78 60 20 68 61 73 20 6e 6f 74 20 62 65 65 6e 20 6d 6f 64 69 66 69 .........`x`.has.not.been.modifi
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92e80 3e 3e 3e 20 79 20 69 73 20 78 0a 20 20 20 20 20 20 20 20 54 72 75 65 0a 20 20 20 20 20 20 20 20 >>>.y.is.x.........True.........
92ea0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 6e 6f 6e 63 65 6e 74 .........................noncent
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93020 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d ...........Parameters.........--
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93640 20 46 72 6f 6d 20 4d 61 74 68 57 6f 72 6c 64 2d 2d 41 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 .From.MathWorld--A.Wolfram.Web.R
93660 65 73 6f 75 72 63 65 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d esource.................http://m
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936c0 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 4e 6f 6e 63 65 6e 74 72 61 6c 20 46 2d 64 69 73 74 72 ].Wikipedia,."Noncentral.F-distr
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93720 6c 5f 46 2d 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c l_F-distribution..........Exampl
93740 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 49 6e 20 61 es.........--------.........In.a
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93860 20 68 79 70 6f 74 68 65 73 69 73 2e 20 20 57 65 27 6c 6c 20 70 6c 6f 74 20 74 68 65 20 74 77 6f .hypothesis...We'll.plot.the.two
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93a00 28 64 66 6e 75 6d 2c 20 64 66 64 65 6e 2c 20 31 30 30 30 30 30 30 29 0a 20 20 20 20 20 20 20 20 (dfnum,.dfden,.1000000).........
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93a60 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a import.matplotlib.pyplot.as.plt.
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93b40 0a 20 20 20 20 20 20 20 20 7a 69 70 66 28 61 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 .........zipf(a,.size=None).....
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93f20 5a 69 70 66 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 Zipf.distribution...........See.
93f40 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 Also.........--------.........sc
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94020 74 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 6b 29 20 tion.is.............math::.p(k).
94040 3d 20 5c 66 72 61 63 7b 6b 5e 7b 2d 61 7d 7d 7b 5c 7a 65 74 61 28 61 29 7d 2c 0a 0a 20 20 20 20 =.\frac{k^{-a}}{\zeta(a)},......
94060 20 20 20 20 66 6f 72 20 69 6e 74 65 67 65 72 73 20 3a 6d 61 74 68 3a 60 6b 20 5c 67 65 71 20 31 ....for.integers.:math:`k.\geq.1
94080 60 2c 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 5c 7a 65 74 61 60 20 69 73 20 74 68 65 20 52 69 `,.where.:math:`\zeta`.is.the.Ri
940a0 65 6d 61 6e 6e 20 5a 65 74 61 0a 20 20 20 20 20 20 20 20 66 75 6e 63 74 69 6f 6e 2e 0a 0a 20 20 emann.Zeta.........function.....
940c0 20 20 20 20 20 20 49 74 20 69 73 20 6e 61 6d 65 64 20 66 6f 72 20 74 68 65 20 41 6d 65 72 69 63 ......It.is.named.for.the.Americ
940e0 61 6e 20 6c 69 6e 67 75 69 73 74 20 47 65 6f 72 67 65 20 4b 69 6e 67 73 6c 65 79 20 5a 69 70 66 an.linguist.George.Kingsley.Zipf
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94140 66 20 61 20 6c 61 6e 67 75 61 67 65 20 69 73 20 69 6e 76 65 72 73 65 6c 79 0a 20 20 20 20 20 20 f.a.language.is.inversely.......
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94180 65 20 66 72 65 71 75 65 6e 63 79 20 74 61 62 6c 65 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 e.frequency.table...........Refe
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941c0 20 20 2e 2e 20 5b 31 5d 20 5a 69 70 66 2c 20 47 2e 20 4b 2e 2c 20 22 53 65 6c 65 63 74 65 64 20 .....[1].Zipf,.G..K.,."Selected.
941e0 53 74 75 64 69 65 73 20 6f 66 20 74 68 65 20 50 72 69 6e 63 69 70 6c 65 20 6f 66 20 52 65 6c 61 Studies.of.the.Principle.of.Rela
94200 74 69 76 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 46 72 65 71 75 65 6e 63 79 20 69 6e tive................Frequency.in
94220 20 4c 61 6e 67 75 61 67 65 2c 22 20 43 61 6d 62 72 69 64 67 65 2c 20 4d 41 3a 20 48 61 72 76 61 .Language,".Cambridge,.MA:.Harva
94240 72 64 20 55 6e 69 76 2e 20 50 72 65 73 73 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 31 rd.Univ..Press,................1
94260 39 33 32 2e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 932...........Examples.........-
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94340 70 6c 65 73 2c 20 61 6c 6f 6e 67 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 74 68 65 20 65 78 70 ples,.along.with.........the.exp
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94400 63 74 65 73 74 3a 20 2b 53 4b 49 50 0a 0a 20 20 20 20 20 20 20 20 60 62 69 6e 63 6f 75 6e 74 60 ctest:.+SKIP..........`bincount`
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94440 6d 61 6c 6c 20 69 6e 74 65 67 65 72 73 2e 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 63 6f 75 6e mall.integers...........>>>.coun
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944e0 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 70 6c 6f 74 28 6b 2c 20 6e 2a 28 6b 2a 2a 2d .........>>>.plt.plot(k,.n*(k**-
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94520 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 20 20 20 20 20 6c 61 62 65 6c 3d 27 65 78 70 65 63 74 ...................label='expect
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94560 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 73 65 6d 69 6c 6f 67 79 28 29 0a 20 20 20 20 20 20 20 ......>>>.plt.semilogy()........
94580 20 3e 3e 3e 20 70 6c 74 2e 67 72 69 64 28 61 6c 70 68 61 3d 30 2e 34 29 0a 20 20 20 20 20 20 20 .>>>.plt.grid(alpha=0.4)........
945a0 20 3e 3e 3e 20 70 6c 74 2e 6c 65 67 65 6e 64 28 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c .>>>.plt.legend().........>>>.pl
945c0 74 2e 74 69 74 6c 65 28 66 27 5a 69 70 66 20 73 61 6d 70 6c 65 2c 20 61 3d 7b 61 7d 2c 20 73 69 t.title(f'Zipf.sample,.a={a},.si
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94600 0a 20 20 20 20 20 20 20 20 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 70 6f 69 73 73 6f 6e .........................poisson
94620 28 6c 61 6d 3d 31 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 (lam=1.0,.size=None)..........Dr
94640 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 50 6f 69 73 73 6f 6e 20 64 69 73 74 72 69 aw.samples.from.a.Poisson.distri
94660 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 50 6f 69 73 73 6f 6e 20 64 69 73 bution...........The.Poisson.dis
94680 74 72 69 62 75 74 69 6f 6e 20 69 73 20 74 68 65 20 6c 69 6d 69 74 20 6f 66 20 74 68 65 20 62 69 tribution.is.the.limit.of.the.bi
946a0 6e 6f 6d 69 61 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 66 6f 72 20 nomial.distribution.........for.
946c0 6c 61 72 67 65 20 4e 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 large.N...........Parameters....
946e0 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6c 61 6d 20 3a 20 66 6c .....----------.........lam.:.fl
94700 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 oat.or.array_like.of.floats.....
94720 20 20 20 20 20 20 20 20 45 78 70 65 63 74 65 64 20 6e 75 6d 62 65 72 20 6f 66 20 65 76 65 6e 74 ........Expected.number.of.event
94740 73 20 6f 63 63 75 72 72 69 6e 67 20 69 6e 20 61 20 66 69 78 65 64 2d 74 69 6d 65 20 69 6e 74 65 s.occurring.in.a.fixed-time.inte
94760 72 76 61 6c 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 6d 75 73 74 20 62 65 20 3e 3d 20 30 2e 20 rval,.............must.be.>=.0..
94780 41 20 73 65 71 75 65 6e 63 65 20 6d 75 73 74 20 62 65 20 62 72 6f 61 64 63 61 73 74 61 62 6c 65 A.sequence.must.be.broadcastable
947a0 20 6f 76 65 72 20 74 68 65 20 72 65 71 75 65 73 74 65 64 0a 20 20 20 20 20 20 20 20 20 20 20 20 .over.the.requested.............
947c0 73 69 7a 65 2e 0a 20 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c size..........size.:.int.or.tupl
947e0 65 20 6f 66 20 69 6e 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 e.of.ints,.optional.............
94800 4f 75 74 70 75 74 20 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 Output.shape...If.the.given.shap
94820 65 20 69 73 2c 20 65 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a e.is,.e.g.,.``(m,.n,.k)``,.then.
94840 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 ............``m.*.n.*.k``.sample
94860 73 20 61 72 65 20 64 72 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 s.are.drawn...If.size.is.``None`
94880 60 20 28 64 65 66 61 75 6c 74 29 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c `.(default),.............a.singl
948a0 65 20 76 61 6c 75 65 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 6c 61 6d 60 60 20 69 e.value.is.returned.if.``lam``.i
948c0 73 20 61 20 73 63 61 6c 61 72 2e 20 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 s.a.scalar..Otherwise,..........
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94900 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 s.are.drawn...........Returns...
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94940 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 ray.or.scalar.............Drawn.
94960 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 50 samples.from.the.parameterized.P
94980 6f 69 73 73 6f 6e 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f oisson.distribution...........No
949a0 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 50 6f tes.........-----.........The.Po
949c0 69 73 73 6f 6e 20 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d isson.distribution.............m
949e0 61 74 68 3a 3a 20 66 28 6b 3b 20 5c 6c 61 6d 62 64 61 29 3d 5c 66 72 61 63 7b 5c 6c 61 6d 62 64 ath::.f(k;.\lambda)=\frac{\lambd
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94b20 73 20 6c 69 6d 69 74 65 64 20 74 6f 20 74 68 65 20 72 61 6e 67 65 20 6f 66 20 74 68 65 20 43 20 s.limited.to.the.range.of.the.C.
94b40 69 6e 74 36 34 20 74 79 70 65 2c 20 61 0a 20 20 20 20 20 20 20 20 56 61 6c 75 65 45 72 72 6f 72 int64.type,.a.........ValueError
94b60 20 69 73 20 72 61 69 73 65 64 20 77 68 65 6e 20 60 6c 61 6d 60 20 69 73 20 77 69 74 68 69 6e 20 .is.raised.when.`lam`.is.within.
94b80 31 30 20 73 69 67 6d 61 20 6f 66 20 74 68 65 20 6d 61 78 69 6d 75 6d 0a 20 20 20 20 20 20 20 20 10.sigma.of.the.maximum.........
94ba0 72 65 70 72 65 73 65 6e 74 61 62 6c 65 20 76 61 6c 75 65 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 representable.value...........Re
94bc0 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 ferences.........----------.....
94be0 20 20 20 20 2e 2e 20 5b 31 5d 20 57 65 69 73 73 74 65 69 6e 2c 20 45 72 69 63 20 57 2e 20 22 50 .......[1].Weisstein,.Eric.W.."P
94c00 6f 69 73 73 6f 6e 20 44 69 73 74 72 69 62 75 74 69 6f 6e 2e 22 0a 20 20 20 20 20 20 20 20 20 20 oisson.Distribution."...........
94c20 20 20 20 20 20 46 72 6f 6d 20 4d 61 74 68 57 6f 72 6c 64 2d 2d 41 20 57 6f 6c 66 72 61 6d 20 57 .....From.MathWorld--A.Wolfram.W
94c40 65 62 20 52 65 73 6f 75 72 63 65 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 eb.Resource.................http
94c60 3a 2f 2f 6d 61 74 68 77 6f 72 6c 64 2e 77 6f 6c 66 72 61 6d 2e 63 6f 6d 2f 50 6f 69 73 73 6f 6e ://mathworld.wolfram.com/Poisson
94c80 44 69 73 74 72 69 62 75 74 69 6f 6e 2e 68 74 6d 6c 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 32 5d Distribution.html............[2]
94ca0 20 57 69 6b 69 70 65 64 69 61 2c 20 22 50 6f 69 73 73 6f 6e 20 64 69 73 74 72 69 62 75 74 69 6f .Wikipedia,."Poisson.distributio
94cc0 6e 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 n",................https://en.wi
94ce0 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 50 6f 69 73 73 6f 6e 5f 64 69 73 74 72 69 62 kipedia.org/wiki/Poisson_distrib
94d00 75 74 69 6f 6e 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 ution..........Examples.........
94d20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 --------.........Draw.samples.fr
94d40 6f 6d 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e om.the.distribution:..........>>
94d60 3e 20 69 6d 70 6f 72 74 20 6e 75 6d 70 79 20 61 73 20 6e 70 0a 20 20 20 20 20 20 20 20 3e 3e 3e >.import.numpy.as.np.........>>>
94d80 20 72 6e 67 20 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 .rng.=.np.random.default_rng()..
94da0 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 72 6e 67 2e 70 6f 69 73 73 6f 6e 28 35 2c 20 31 30 .......>>>.s.=.rng.poisson(5,.10
94dc0 30 30 30 29 0a 0a 20 20 20 20 20 20 20 20 44 69 73 70 6c 61 79 20 68 69 73 74 6f 67 72 61 6d 20 000)..........Display.histogram.
94de0 6f 66 20 74 68 65 20 73 61 6d 70 6c 65 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 69 6d 70 6f of.the.sample:..........>>>.impo
94e00 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f 74 20 61 73 20 70 6c 74 0a 20 20 20 20 rt.matplotlib.pyplot.as.plt.....
94e20 20 20 20 20 3e 3e 3e 20 63 6f 75 6e 74 2c 20 62 69 6e 73 2c 20 69 67 6e 6f 72 65 64 20 3d 20 70 ....>>>.count,.bins,.ignored.=.p
94e40 6c 74 2e 68 69 73 74 28 73 2c 20 31 34 2c 20 64 65 6e 73 69 74 79 3d 54 72 75 65 29 0a 20 20 20 lt.hist(s,.14,.density=True)....
94e60 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 .....>>>.plt.show()..........Dra
94e80 77 20 65 61 63 68 20 31 30 30 20 76 61 6c 75 65 73 20 66 6f 72 20 6c 61 6d 62 64 61 20 31 30 30 w.each.100.values.for.lambda.100
94ea0 20 61 6e 64 20 35 30 30 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 72 6e 67 2e 70 .and.500:..........>>>.s.=.rng.p
94ec0 6f 69 73 73 6f 6e 28 6c 61 6d 3d 28 31 30 30 2e 2c 20 35 30 30 2e 29 2c 20 73 69 7a 65 3d 28 31 oisson(lam=(100.,.500.),.size=(1
94ee0 30 30 2c 20 32 29 29 0a 0a 20 20 20 20 20 20 20 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00,.2)).........................
94f00 0a 20 20 20 20 20 20 20 20 67 75 6d 62 65 6c 28 6c 6f 63 3d 30 2e 30 2c 20 73 63 61 6c 65 3d 31 .........gumbel(loc=0.0,.scale=1
94f20 2e 30 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d .0,.size=None)..........Draw.sam
94f40 70 6c 65 73 20 66 72 6f 6d 20 61 20 47 75 6d 62 65 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e ples.from.a.Gumbel.distribution.
94f60 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 47 75 ..........Draw.samples.from.a.Gu
94f80 6d 62 65 6c 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 77 69 74 68 20 73 70 65 63 69 66 69 65 64 mbel.distribution.with.specified
94fa0 20 6c 6f 63 61 74 69 6f 6e 20 61 6e 64 0a 20 20 20 20 20 20 20 20 73 63 61 6c 65 2e 20 20 46 6f .location.and.........scale...Fo
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94fe0 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2c 20 73 65 65 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 .distribution,.see.........Notes
95000 20 61 6e 64 20 52 65 66 65 72 65 6e 63 65 73 20 62 65 6c 6f 77 2e 0a 0a 20 20 20 20 20 20 20 20 .and.References.below...........
95020 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 Parameters.........----------...
95040 20 20 20 20 20 20 6c 6f 63 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 ......loc.:.float.or.array_like.
95060 6f 66 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 of.floats,.optional.............
95080 54 68 65 20 6c 6f 63 61 74 69 6f 6e 20 6f 66 20 74 68 65 20 6d 6f 64 65 20 6f 66 20 74 68 65 20 The.location.of.the.mode.of.the.
950a0 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 20 44 65 66 61 75 6c 74 20 69 73 20 30 2e 0a 20 20 20 20 distribution..Default.is.0......
950c0 20 20 20 20 73 63 61 6c 65 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 ....scale.:.float.or.array_like.
950e0 6f 66 20 66 6c 6f 61 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 of.floats,.optional.............
95100 54 68 65 20 73 63 61 6c 65 20 70 61 72 61 6d 65 74 65 72 20 6f 66 20 74 68 65 20 64 69 73 74 72 The.scale.parameter.of.the.distr
95120 69 62 75 74 69 6f 6e 2e 20 44 65 66 61 75 6c 74 20 69 73 20 31 2e 20 4d 75 73 74 20 62 65 20 6e ibution..Default.is.1..Must.be.n
95140 6f 6e 2d 0a 20 20 20 20 20 20 20 20 20 20 20 20 6e 65 67 61 74 69 76 65 2e 0a 20 20 20 20 20 20 on-.............negative........
95160 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e 74 73 2c 20 6f ..size.:.int.or.tuple.of.ints,.o
95180 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 73 68 61 70 65 ptional.............Output.shape
951a0 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 2e 67 2e 2c 20 ...If.the.given.shape.is,.e.g.,.
951c0 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 20 20 20 20 ``(m,.n,.k)``,.then.............
951e0 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e ``m.*.n.*.k``.samples.are.drawn.
95200 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 75 6c 74 29 2c ..If.size.is.``None``.(default),
95220 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 20 69 73 20 72 .............a.single.value.is.r
95240 65 74 75 72 6e 65 64 20 69 66 20 60 60 6c 6f 63 60 60 20 61 6e 64 20 60 60 73 63 61 6c 65 60 60 eturned.if.``loc``.and.``scale``
95260 20 61 72 65 20 62 6f 74 68 20 73 63 61 6c 61 72 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f .are.both.scalars..............O
95280 74 68 65 72 77 69 73 65 2c 20 60 60 6e 70 2e 62 72 6f 61 64 63 61 73 74 28 6c 6f 63 2c 20 73 63 therwise,.``np.broadcast(loc,.sc
952a0 61 6c 65 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 61 77 6e 2e 0a 0a ale).size``.samples.are.drawn...
952c0 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a ........Returns.........-------.
952e0 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 63 61 6c 61 72 0a ........out.:.ndarray.or.scalar.
95300 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 ............Drawn.samples.from.t
95320 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 47 75 6d 62 65 6c 20 64 69 73 74 72 69 62 75 he.parameterized.Gumbel.distribu
95340 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 20 20 20 20 tion...........See.Also.........
95360 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 67 75 6d --------.........scipy.stats.gum
95380 62 65 6c 5f 6c 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 67 75 6d 62 65 6c bel_l.........scipy.stats.gumbel
953a0 5f 72 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e 73 74 61 74 73 2e 67 65 6e 65 78 74 72 65 6d _r.........scipy.stats.genextrem
953c0 65 0a 20 20 20 20 20 20 20 20 77 65 69 62 75 6c 6c 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 e.........weibull..........Notes
953e0 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 47 75 6d 62 65 .........-----.........The.Gumbe
95400 6c 20 28 6f 72 20 53 6d 61 6c 6c 65 73 74 20 45 78 74 72 65 6d 65 20 56 61 6c 75 65 20 28 53 45 l.(or.Smallest.Extreme.Value.(SE
95420 56 29 20 6f 72 20 74 68 65 20 53 6d 61 6c 6c 65 73 74 20 45 78 74 72 65 6d 65 0a 20 20 20 20 20 V).or.the.Smallest.Extreme......
95440 20 20 20 56 61 6c 75 65 20 54 79 70 65 20 49 29 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 ...Value.Type.I).distribution.is
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954e0 6d 62 65 6c 20 69 73 20 61 20 73 70 65 63 69 61 6c 20 63 61 73 65 20 6f 66 20 74 68 65 20 45 78 mbel.is.a.special.case.of.the.Ex
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95520 20 20 20 20 20 20 20 20 66 6f 72 20 6d 61 78 69 6d 75 6d 73 20 66 72 6f 6d 20 64 69 73 74 72 69 ........for.maximums.from.distri
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95560 74 61 69 6c 73 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 tails...........The.probability.
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955a0 69 6f 6e 20 69 73 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d ion.is.............math::.p(x).=
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95620 72 65 20 3a 6d 61 74 68 3a 60 5c 6d 75 60 20 69 73 20 74 68 65 20 6d 6f 64 65 2c 20 61 20 6c 6f re.:math:`\mu`.is.the.mode,.a.lo
95640 63 61 74 69 6f 6e 20 70 61 72 61 6d 65 74 65 72 2c 20 61 6e 64 0a 20 20 20 20 20 20 20 20 3a 6d cation.parameter,.and.........:m
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95680 65 72 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 47 75 6d 62 65 6c 20 28 6e 61 6d 65 64 20 66 er...........The.Gumbel.(named.f
956a0 6f 72 20 47 65 72 6d 61 6e 20 6d 61 74 68 65 6d 61 74 69 63 69 61 6e 20 45 6d 69 6c 20 4a 75 6c or.German.mathematician.Emil.Jul
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95720 20 6f 66 0a 20 20 20 20 20 20 20 20 66 6c 6f 6f 64 20 65 76 65 6e 74 73 2e 20 49 74 20 69 73 20 .of.........flood.events..It.is.
95740 61 6c 73 6f 20 75 73 65 64 20 66 6f 72 20 6d 6f 64 65 6c 69 6e 67 20 6d 61 78 69 6d 75 6d 20 77 also.used.for.modeling.maximum.w
95760 69 6e 64 20 73 70 65 65 64 20 61 6e 64 0a 20 20 20 20 20 20 20 20 72 61 69 6e 66 61 6c 6c 20 72 ind.speed.and.........rainfall.r
95780 61 74 65 73 2e 20 20 49 74 20 69 73 20 61 20 22 66 61 74 2d 74 61 69 6c 65 64 22 20 64 69 73 74 ates...It.is.a."fat-tailed".dist
957a0 72 69 62 75 74 69 6f 6e 20 2d 20 74 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 6f 66 0a 20 20 ribution.-.the.probability.of...
957c0 20 20 20 20 20 20 61 6e 20 65 76 65 6e 74 20 69 6e 20 74 68 65 20 74 61 69 6c 20 6f 66 20 74 68 ......an.event.in.the.tail.of.th
957e0 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 20 6c 61 72 67 65 72 20 74 68 61 6e 20 69 66 e.distribution.is.larger.than.if
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958a0 20 20 20 20 20 20 20 20 75 6e 64 65 72 65 73 74 69 6d 61 74 65 64 20 74 68 65 20 66 72 65 71 75 ........underestimated.the.frequ
958c0 65 6e 63 79 20 6f 66 20 65 78 74 72 65 6d 65 20 65 76 65 6e 74 73 2e 0a 0a 20 20 20 20 20 20 20 ency.of.extreme.events..........
958e0 20 49 74 20 69 73 20 6f 6e 65 20 6f 66 20 61 20 63 6c 61 73 73 20 6f 66 20 65 78 74 72 65 6d 65 .It.is.one.of.a.class.of.extreme
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95960 75 64 65 73 20 74 68 65 20 57 65 69 62 75 6c 6c 20 61 6e 64 0a 20 20 20 20 20 20 20 20 46 72 65 udes.the.Weibull.and.........Fre
95980 63 68 65 74 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 20 68 61 73 20 chet...........The.function.has.
959a0 61 20 6d 65 61 6e 20 6f 66 20 3a 6d 61 74 68 3a 60 5c 6d 75 20 2b 20 30 2e 35 37 37 32 31 5c 62 a.mean.of.:math:`\mu.+.0.57721\b
959c0 65 74 61 60 20 61 6e 64 20 61 20 76 61 72 69 61 6e 63 65 0a 20 20 20 20 20 20 20 20 6f 66 20 3a eta`.and.a.variance.........of.:
959e0 6d 61 74 68 3a 60 5c 66 72 61 63 7b 5c 70 69 5e 32 7d 7b 36 7d 5c 62 65 74 61 5e 32 60 2e 0a 0a math:`\frac{\pi^2}{6}\beta^2`...
95a00 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d ........References.........-----
95a20 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 47 75 6d 62 65 6c 2c 20 45 2e 20 -----............[1].Gumbel,.E..
95a40 4a 2e 2c 20 22 53 74 61 74 69 73 74 69 63 73 20 6f 66 20 45 78 74 72 65 6d 65 73 2c 22 0a 20 20 J.,."Statistics.of.Extremes,"...
95a60 20 20 20 20 20 20 20 20 20 20 20 20 20 4e 65 77 20 59 6f 72 6b 3a 20 43 6f 6c 75 6d 62 69 61 20 .............New.York:.Columbia.
95a80 55 6e 69 76 65 72 73 69 74 79 20 50 72 65 73 73 2c 20 31 39 35 38 2e 0a 20 20 20 20 20 20 20 20 University.Press,.1958..........
95aa0 2e 2e 20 5b 32 5d 20 52 65 69 73 73 2c 20 52 2e 2d 44 2e 20 61 6e 64 20 54 68 6f 6d 61 73 2c 20 ...[2].Reiss,.R.-D..and.Thomas,.
95ac0 4d 2e 2c 20 22 53 74 61 74 69 73 74 69 63 61 6c 20 41 6e 61 6c 79 73 69 73 20 6f 66 20 45 78 74 M.,."Statistical.Analysis.of.Ext
95ae0 72 65 6d 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 56 61 6c 75 65 73 20 66 72 6f 6d 20 reme................Values.from.
95b00 49 6e 73 75 72 61 6e 63 65 2c 20 46 69 6e 61 6e 63 65 2c 20 48 79 64 72 6f 6c 6f 67 79 20 61 6e Insurance,.Finance,.Hydrology.an
95b20 64 20 4f 74 68 65 72 20 46 69 65 6c 64 73 2c 22 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 d.Other.Fields,"................
95b40 42 61 73 65 6c 3a 20 42 69 72 6b 68 61 75 73 65 72 20 56 65 72 6c 61 67 2c 20 32 30 30 31 2e 0a Basel:.Birkhauser.Verlag,.2001..
95b60 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d .........Examples.........------
95b80 2d 2d 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 74 68 65 --.........Draw.samples.from.the
95ba0 20 64 69 73 74 72 69 62 75 74 69 6f 6e 3a 0a 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 72 6e 67 20 .distribution:..........>>>.rng.
95bc0 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 20 20 20 20 20 =.np.random.default_rng().......
95be0 20 20 3e 3e 3e 20 6d 75 2c 20 62 65 74 61 20 3d 20 30 2c 20 30 2e 31 20 23 20 6c 6f 63 61 74 69 ..>>>.mu,.beta.=.0,.0.1.#.locati
95c00 6f 6e 20 61 6e 64 20 73 63 61 6c 65 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 73 20 3d 20 72 6e 67 on.and.scale.........>>>.s.=.rng
95c20 2e 67 75 6d 62 65 6c 28 6d 75 2c 20 62 65 74 61 2c 20 31 30 30 30 29 0a 0a 20 20 20 20 20 20 20 .gumbel(mu,.beta,.1000).........
95c40 20 44 69 73 70 6c 61 79 20 74 68 65 20 68 69 73 74 6f 67 72 61 6d 20 6f 66 20 74 68 65 20 73 61 .Display.the.histogram.of.the.sa
95c60 6d 70 6c 65 73 2c 20 61 6c 6f 6e 67 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 74 68 65 20 70 72 mples,.along.with.........the.pr
95c80 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 6e 63 74 69 6f 6e 3a 0a 0a 20 20 20 obability.density.function:.....
95ca0 20 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 6d 61 74 70 6c 6f 74 6c 69 62 2e 70 79 70 6c 6f .....>>>.import.matplotlib.pyplo
95cc0 74 20 61 73 20 70 6c 74 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 63 6f 75 6e 74 2c 20 62 69 6e 73 t.as.plt.........>>>.count,.bins
95ce0 2c 20 69 67 6e 6f 72 65 64 20 3d 20 70 6c 74 2e 68 69 73 74 28 73 2c 20 33 30 2c 20 64 65 6e 73 ,.ignored.=.plt.hist(s,.30,.dens
95d00 69 74 79 3d 54 72 75 65 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 70 6c 6f 74 28 62 ity=True).........>>>.plt.plot(b
95d20 69 6e 73 2c 20 28 31 2f 62 65 74 61 29 2a 6e 70 2e 65 78 70 28 2d 28 62 69 6e 73 20 2d 20 6d 75 ins,.(1/beta)*np.exp(-(bins.-.mu
95d40 29 2f 62 65 74 61 29 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 20 20 20 20 20 2a 20 6e )/beta)......................*.n
95d60 70 2e 65 78 70 28 20 2d 6e 70 2e 65 78 70 28 20 2d 28 62 69 6e 73 20 2d 20 6d 75 29 20 2f 62 65 p.exp(.-np.exp(.-(bins.-.mu)./be
95d80 74 61 29 20 29 2c 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 20 20 20 20 20 20 6c 69 6e 65 ta).),......................line
95da0 77 69 64 74 68 3d 32 2c 20 63 6f 6c 6f 72 3d 27 72 27 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 width=2,.color='r').........>>>.
95dc0 70 6c 74 2e 73 68 6f 77 28 29 0a 0a 20 20 20 20 20 20 20 20 53 68 6f 77 20 68 6f 77 20 61 6e 20 plt.show()..........Show.how.an.
95de0 65 78 74 72 65 6d 65 20 76 61 6c 75 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 63 61 6e 20 61 extreme.value.distribution.can.a
95e00 72 69 73 65 20 66 72 6f 6d 20 61 20 47 61 75 73 73 69 61 6e 20 70 72 6f 63 65 73 73 0a 20 20 20 rise.from.a.Gaussian.process....
95e20 20 20 20 20 20 61 6e 64 20 63 6f 6d 70 61 72 65 20 74 6f 20 61 20 47 61 75 73 73 69 61 6e 3a 0a .....and.compare.to.a.Gaussian:.
95e40 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6d 65 61 6e 73 20 3d 20 5b 5d 0a 20 20 20 20 20 20 20 20 .........>>>.means.=.[].........
95e60 3e 3e 3e 20 6d 61 78 69 6d 61 20 3d 20 5b 5d 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 66 6f 72 20 >>>.maxima.=.[].........>>>.for.
95e80 69 20 69 6e 20 72 61 6e 67 65 28 30 2c 31 30 30 30 29 20 3a 0a 20 20 20 20 20 20 20 20 2e 2e 2e i.in.range(0,1000).:............
95ea0 20 20 20 20 61 20 3d 20 72 6e 67 2e 6e 6f 72 6d 61 6c 28 6d 75 2c 20 62 65 74 61 2c 20 31 30 30 ....a.=.rng.normal(mu,.beta,.100
95ec0 30 29 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 6d 65 61 6e 73 2e 61 70 70 65 6e 64 28 61 0)................means.append(a
95ee0 2e 6d 65 61 6e 28 29 29 0a 20 20 20 20 20 20 20 20 2e 2e 2e 20 20 20 20 6d 61 78 69 6d 61 2e 61 .mean())................maxima.a
95f00 70 70 65 6e 64 28 61 2e 6d 61 78 28 29 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 63 6f 75 6e 74 ppend(a.max()).........>>>.count
95f20 2c 20 62 69 6e 73 2c 20 69 67 6e 6f 72 65 64 20 3d 20 70 6c 74 2e 68 69 73 74 28 6d 61 78 69 6d ,.bins,.ignored.=.plt.hist(maxim
95f40 61 2c 20 33 30 2c 20 64 65 6e 73 69 74 79 3d 54 72 75 65 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e a,.30,.density=True).........>>>
95f60 20 62 65 74 61 20 3d 20 6e 70 2e 73 74 64 28 6d 61 78 69 6d 61 29 20 2a 20 6e 70 2e 73 71 72 74 .beta.=.np.std(maxima).*.np.sqrt
95f80 28 36 29 20 2f 20 6e 70 2e 70 69 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 6d 75 20 3d 20 6e 70 2e (6)./.np.pi.........>>>.mu.=.np.
95fa0 6d 65 61 6e 28 6d 61 78 69 6d 61 29 20 2d 20 30 2e 35 37 37 32 31 2a 62 65 74 61 0a 20 20 20 20 mean(maxima).-.0.57721*beta.....
95fc0 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 70 6c 6f 74 28 62 69 6e 73 2c 20 28 31 2f 62 65 74 61 29 2a ....>>>.plt.plot(bins,.(1/beta)*
95fe0 6e 70 2e 65 78 70 28 2d 28 62 69 6e 73 20 2d 20 6d 75 29 2f 62 65 74 61 29 0a 20 20 20 20 20 20 np.exp(-(bins.-.mu)/beta).......
96000 20 20 2e 2e 2e 20 20 20 20 20 20 20 20 20 20 2a 20 6e 70 2e 65 78 70 28 2d 6e 70 2e 65 78 70 28 ...............*.np.exp(-np.exp(
96020 2d 28 62 69 6e 73 20 2d 20 6d 75 29 2f 62 65 74 61 29 29 2c 0a 20 20 20 20 20 20 20 20 2e 2e 2e -(bins.-.mu)/beta)),............
96040 20 20 20 20 20 20 20 20 20 20 6c 69 6e 65 77 69 64 74 68 3d 32 2c 20 63 6f 6c 6f 72 3d 27 72 27 ..........linewidth=2,.color='r'
96060 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 70 6c 6f 74 28 62 69 6e 73 2c 20 31 2f 28 ).........>>>.plt.plot(bins,.1/(
96080 62 65 74 61 20 2a 20 6e 70 2e 73 71 72 74 28 32 20 2a 20 6e 70 2e 70 69 29 29 0a 20 20 20 20 20 beta.*.np.sqrt(2.*.np.pi))......
960a0 20 20 20 2e 2e 2e 20 20 20 20 20 20 20 20 20 20 2a 20 6e 70 2e 65 78 70 28 2d 28 62 69 6e 73 20 ................*.np.exp(-(bins.
960c0 2d 20 6d 75 29 2a 2a 32 20 2f 20 28 32 20 2a 20 62 65 74 61 2a 2a 32 29 29 2c 0a 20 20 20 20 20 -.mu)**2./.(2.*.beta**2)),......
960e0 20 20 20 2e 2e 2e 20 20 20 20 20 20 20 20 20 20 6c 69 6e 65 77 69 64 74 68 3d 32 2c 20 63 6f 6c ................linewidth=2,.col
96100 6f 72 3d 27 67 27 29 0a 20 20 20 20 20 20 20 20 3e 3e 3e 20 70 6c 74 2e 73 68 6f 77 28 29 0a 0a or='g').........>>>.plt.show()..
96120 20 20 20 20 20 20 20 20 00 00 00 00 00 00 00 00 40 cc 07 80 01 00 00 00 d0 c2 01 80 01 00 00 00 ................@...............
96140 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 50 cc 07 80 01 00 00 00 f0 bf 01 80 01 00 00 00 ................P...............
96160 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 04 c5 07 80 01 00 00 00 d0 bb 01 80 01 00 00 00 ................................
96180 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 60 cc 07 80 01 00 00 00 70 b6 01 80 01 00 00 00 ................`.......p.......
961a0 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 70 cc 07 80 01 00 00 00 40 b3 01 80 01 00 00 00 ................p.......@.......
961c0 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 88 cc 07 80 01 00 00 00 40 b2 01 80 01 00 00 00 ........................@.......
961e0 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
96200 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0a 20 20 20 20 20 20 20 20 63 68 69 73 71 75 61 .........................chisqua
96220 72 65 28 64 66 2c 20 73 69 7a 65 3d 4e 6f 6e 65 29 0a 0a 20 20 20 20 20 20 20 20 44 72 61 77 20 re(df,.size=None)..........Draw.
96240 73 61 6d 70 6c 65 73 20 66 72 6f 6d 20 61 20 63 68 69 2d 73 71 75 61 72 65 20 64 69 73 74 72 69 samples.from.a.chi-square.distri
96260 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 57 68 65 6e 20 60 64 66 60 20 69 6e 64 65 70 bution...........When.`df`.indep
96280 65 6e 64 65 6e 74 20 72 61 6e 64 6f 6d 20 76 61 72 69 61 62 6c 65 73 2c 20 65 61 63 68 20 77 69 endent.random.variables,.each.wi
962a0 74 68 20 73 74 61 6e 64 61 72 64 20 6e 6f 72 6d 61 6c 0a 20 20 20 20 20 20 20 20 64 69 73 74 72 th.standard.normal.........distr
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962e0 72 65 20 73 71 75 61 72 65 64 20 61 6e 64 20 73 75 6d 6d 65 64 2c 20 74 68 65 0a 20 20 20 20 20 re.squared.and.summed,.the......
96300 20 20 20 72 65 73 75 6c 74 69 6e 67 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 69 73 20 63 68 69 ...resulting.distribution.is.chi
96320 2d 73 71 75 61 72 65 20 28 73 65 65 20 4e 6f 74 65 73 29 2e 20 20 54 68 69 73 20 64 69 73 74 72 -square.(see.Notes)...This.distr
96340 69 62 75 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 69 73 20 6f 66 74 65 6e 20 75 73 65 64 20 69 6e ibution.........is.often.used.in
96360 20 68 79 70 6f 74 68 65 73 69 73 20 74 65 73 74 69 6e 67 2e 0a 0a 20 20 20 20 20 20 20 20 50 61 .hypothesis.testing...........Pa
96380 72 61 6d 65 74 65 72 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 rameters.........----------.....
963a0 20 20 20 20 64 66 20 3a 20 66 6c 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 ....df.:.float.or.array_like.of.
963c0 66 6c 6f 61 74 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 4e 75 6d 62 65 72 20 6f 66 20 64 65 floats..............Number.of.de
963e0 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 2c 20 6d 75 73 74 20 62 65 20 3e 20 30 2e 0a 20 grees.of.freedom,.must.be.>.0...
96400 20 20 20 20 20 20 20 73 69 7a 65 20 3a 20 69 6e 74 20 6f 72 20 74 75 70 6c 65 20 6f 66 20 69 6e .......size.:.int.or.tuple.of.in
96420 74 73 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 20 20 20 20 4f 75 74 70 75 74 20 ts,.optional.............Output.
96440 73 68 61 70 65 2e 20 20 49 66 20 74 68 65 20 67 69 76 65 6e 20 73 68 61 70 65 20 69 73 2c 20 65 shape...If.the.given.shape.is,.e
96460 2e 67 2e 2c 20 60 60 28 6d 2c 20 6e 2c 20 6b 29 60 60 2c 20 74 68 65 6e 0a 20 20 20 20 20 20 20 .g.,.``(m,.n,.k)``,.then........
96480 20 20 20 20 20 60 60 6d 20 2a 20 6e 20 2a 20 6b 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 .....``m.*.n.*.k``.samples.are.d
964a0 72 61 77 6e 2e 20 20 49 66 20 73 69 7a 65 20 69 73 20 60 60 4e 6f 6e 65 60 60 20 28 64 65 66 61 rawn...If.size.is.``None``.(defa
964c0 75 6c 74 29 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 20 73 69 6e 67 6c 65 20 76 61 6c 75 65 ult),.............a.single.value
964e0 20 69 73 20 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 64 66 60 60 20 69 73 20 61 20 73 63 61 6c .is.returned.if.``df``.is.a.scal
96500 61 72 2e 20 20 4f 74 68 65 72 77 69 73 65 2c 0a 20 20 20 20 20 20 20 20 20 20 20 20 60 60 6e 70 ar...Otherwise,.............``np
96520 2e 61 72 72 61 79 28 64 66 29 2e 73 69 7a 65 60 60 20 73 61 6d 70 6c 65 73 20 61 72 65 20 64 72 .array(df).size``.samples.are.dr
96540 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 2d 2d awn...........Returns.........--
96560 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 20 6f 72 20 73 -----.........out.:.ndarray.or.s
96580 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c 65 73 20 calar.............Drawn.samples.
965a0 66 72 6f 6d 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 69 7a 65 64 20 63 68 69 2d 73 71 75 61 72 from.the.parameterized.chi-squar
965c0 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 61 69 73 65 73 0a e.distribution...........Raises.
965e0 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 56 61 6c 75 65 45 72 72 6f ........------.........ValueErro
96600 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 57 68 65 6e 20 60 64 66 60 20 3c 3d 20 30 20 6f 72 20 r.............When.`df`.<=.0.or.
96620 77 68 65 6e 20 61 6e 20 69 6e 61 70 70 72 6f 70 72 69 61 74 65 20 60 73 69 7a 65 60 20 28 65 2e when.an.inappropriate.`size`.(e.
96640 67 2e 20 60 60 73 69 7a 65 3d 2d 31 60 60 29 0a 20 20 20 20 20 20 20 20 20 20 20 20 69 73 20 67 g..``size=-1``).............is.g
96660 69 76 65 6e 2e 0a 0a 20 20 20 20 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d iven...........Notes.........---
96680 2d 2d 0a 20 20 20 20 20 20 20 20 54 68 65 20 76 61 72 69 61 62 6c 65 20 6f 62 74 61 69 6e 65 64 --.........The.variable.obtained
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96720 5f 7b 69 3d 30 7d 5e 7b 5c 6d 61 74 68 74 74 7b 64 66 7d 7d 20 58 5e 32 5f 69 0a 0a 20 20 20 20 _{i=0}^{\mathtt{df}}.X^2_i......
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96760 65 6e 6f 74 65 64 0a 0a 20 20 20 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 51 20 5c 73 69 6d enoted.............math::.Q.\sim
96780 20 5c 63 68 69 5e 32 5f 6b 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 72 6f 62 61 62 69 6c .\chi^2_k...........The.probabil
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967e0 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 5c 66 72 61 63 7b 28 31 2f 32 29 5e 7b 6b ....math::.p(x).=.\frac{(1/2)^{k
96800 2f 32 7d 7d 7b 5c 47 61 6d 6d 61 28 6b 2f 32 29 7d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 /2}}{\Gamma(k/2)}...............
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96860 73 20 74 68 65 20 67 61 6d 6d 61 20 66 75 6e 63 74 69 6f 6e 2c 0a 0a 20 20 20 20 20 20 20 20 2e s.the.gamma.function,...........
96880 2e 20 6d 61 74 68 3a 3a 20 5c 47 61 6d 6d 61 28 78 29 20 3d 20 5c 69 6e 74 5f 30 5e 7b 2d 5c 69 ..math::.\Gamma(x).=.\int_0^{-\i
968a0 6e 66 74 79 7d 20 74 5e 7b 78 20 2d 20 31 7d 20 65 5e 7b 2d 74 7d 20 64 74 2e 0a 0a 20 20 20 20 nfty}.t^{x.-.1}.e^{-t}.dt.......
968c0 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d ....References.........---------
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96900 6e 67 20 53 74 61 74 69 73 74 69 63 73 20 48 61 6e 64 62 6f 6f 6b 22 0a 20 20 20 20 20 20 20 20 ng.Statistics.Handbook".........
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96940 64 69 76 38 39 38 2f 68 61 6e 64 62 6f 6f 6b 2f 65 64 61 2f 73 65 63 74 69 6f 6e 33 2f 65 64 61 div898/handbook/eda/section3/eda
96960 33 36 36 36 2e 68 74 6d 0a 0a 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 3666.htm..........Examples......
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96b20 6d 69 6e 61 74 6f 72 29 2c 20 77 68 65 72 65 20 62 6f 74 68 20 70 61 72 61 6d 65 74 65 72 73 20 minator),.where.both.parameters.
96b40 6d 75 73 74 20 62 65 20 67 72 65 61 74 65 72 20 74 68 61 6e 0a 20 20 20 20 20 20 20 20 7a 65 72 must.be.greater.than.........zer
96b60 6f 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 72 61 6e 64 6f 6d 20 76 61 72 69 61 74 65 20 6f o...........The.random.variate.o
96b80 66 20 74 68 65 20 46 20 64 69 73 74 72 69 62 75 74 69 6f 6e 20 28 61 6c 73 6f 20 6b 6e 6f 77 6e f.the.F.distribution.(also.known
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96be0 20 64 69 73 74 72 69 62 75 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 74 68 61 74 20 61 72 69 73 65 .distribution.........that.arise
96c00 73 20 69 6e 20 41 4e 4f 56 41 20 74 65 73 74 73 2c 20 61 6e 64 20 69 73 20 74 68 65 20 72 61 74 s.in.ANOVA.tests,.and.is.the.rat
96c20 69 6f 20 6f 66 20 74 77 6f 20 63 68 69 2d 73 71 75 61 72 65 0a 20 20 20 20 20 20 20 20 76 61 72 io.of.two.chi-square.........var
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96c80 6f 61 74 20 6f 72 20 61 72 72 61 79 5f 6c 69 6b 65 20 6f 66 20 66 6c 6f 61 74 73 0a 20 20 20 20 oat.or.array_like.of.floats.....
96ca0 20 20 20 20 20 20 20 20 44 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 20 69 6e 20 6e 75 ........Degrees.of.freedom.in.nu
96cc0 6d 65 72 61 74 6f 72 2c 20 6d 75 73 74 20 62 65 20 3e 20 30 2e 0a 20 20 20 20 20 20 20 20 64 66 merator,.must.be.>.0..........df
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96d00 61 74 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f at.............Degrees.of.freedo
96d20 6d 20 69 6e 20 64 65 6e 6f 6d 69 6e 61 74 6f 72 2c 20 6d 75 73 74 20 62 65 20 3e 20 30 2e 0a 20 m.in.denominator,.must.be.>.0...
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96ea0 20 64 72 61 77 6e 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 .drawn...........Returns........
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96ee0 72 20 73 63 61 6c 61 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 44 72 61 77 6e 20 73 61 6d 70 6c r.scalar.............Drawn.sampl
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96f20 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 53 65 65 20 41 6c 73 6f .distribution...........See.Also
96f40 0a 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 73 63 69 70 79 2e .........--------.........scipy.
96f60 73 74 61 74 73 2e 66 20 3a 20 70 72 6f 62 61 62 69 6c 69 74 79 20 64 65 6e 73 69 74 79 20 66 75 stats.f.:.probability.density.fu
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97040 63 65 73 2e 20 43 61 6c 63 75 6c 61 74 69 6e 67 20 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f ces..Calculating.the.distributio
97060 6e 20 64 65 70 65 6e 64 73 20 6f 6e 20 74 68 65 20 73 61 6d 70 6c 69 6e 67 2c 20 61 6e 64 0a 20 n.depends.on.the.sampling,.and..
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970a0 65 20 72 65 73 70 65 63 74 69 76 65 20 64 65 67 72 65 65 73 20 6f 66 20 66 72 65 65 64 6f 6d 20 e.respective.degrees.of.freedom.
970c0 69 6e 20 74 68 65 0a 20 20 20 20 20 20 20 20 70 72 6f 62 6c 65 6d 2e 20 20 54 68 65 20 76 61 72 in.the.........problem...The.var
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97320 0a 0a 20 20 20 20 20 20 20 20 54 77 6f 20 67 72 6f 75 70 73 2c 20 63 68 69 6c 64 72 65 6e 20 6f ..........Two.groups,.children.o
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973c0 20 20 20 20 20 63 61 73 65 20 67 72 6f 75 70 20 68 61 64 20 61 20 6d 65 61 6e 20 76 61 6c 75 65 .....case.group.had.a.mean.value
973e0 20 6f 66 20 38 36 2e 31 2c 20 63 6f 6e 74 72 6f 6c 73 20 68 61 64 20 61 20 6d 65 61 6e 20 76 61 .of.86.1,.controls.had.a.mean.va
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975e0 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 2e 66 28 64 66 6e 75 =.np.random.default_rng().f(dfnu
97600 6d 2c 20 64 66 64 65 6e 2c 20 31 30 30 30 29 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 6c 6f 77 m,.dfden,.1000)..........The.low
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97760 74 72 69 63 28 63 6f 6c 6f 72 73 2c 20 6e 73 61 6d 70 6c 65 2c 20 73 69 7a 65 3d 4e 6f 6e 65 2c tric(colors,.nsample,.size=None,
97780 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 ................................
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977c0 20 20 47 65 6e 65 72 61 74 65 20 76 61 72 69 61 74 65 73 20 66 72 6f 6d 20 61 20 6d 75 6c 74 69 ..Generate.variates.from.a.multi
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97800 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 6d 75 6c 74 69 76 61 72 69 61 74 65 20 68 ion...........The.multivariate.h
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97840 67 65 6e 65 72 61 6c 69 7a 61 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 6f 66 20 74 68 65 20 68 79 generalization.........of.the.hy
97860 70 65 72 67 65 6f 6d 65 74 72 69 63 20 64 69 73 74 72 69 62 75 74 69 6f 6e 2e 0a 0a 20 20 20 20 pergeometric.distribution.......
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980e0 20 20 20 20 20 66 6f 72 20 61 20 64 65 73 63 72 69 70 74 69 6f 6e 20 6f 66 20 74 68 65 20 6d 65 .....for.a.description.of.the.me
98100 74 68 6f 64 73 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 20 20 20 20 thods...........Returns.........
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9a1a0 20 20 20 20 20 20 20 20 20 57 6f 6c 66 72 61 6d 20 57 65 62 20 52 65 73 6f 75 72 63 65 2e 0a 20 .........Wolfram.Web.Resource...
9a1c0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6d 61 74 68 77 6f 72 6c 64 2e 77 ..............http://mathworld.w
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9b560 64 2e 0a 0a 20 20 20 20 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 20 20 20 20 2d d...........References.........-
9b580 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 20 20 20 20 2e 2e 20 5b 31 5d 20 50 61 70 6f 75 6c 69 ---------............[1].Papouli
9b5a0 73 2c 20 41 2e 2c 20 22 50 72 6f 62 61 62 69 6c 69 74 79 2c 20 52 61 6e 64 6f 6d 20 56 61 72 69 s,.A.,."Probability,.Random.Vari
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9b5e0 20 20 20 20 20 50 72 6f 63 65 73 73 65 73 2c 22 20 33 72 64 20 65 64 2e 2c 20 4e 65 77 20 59 6f .....Processes,".3rd.ed.,.New.Yo
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9b620 2e 20 5b 32 5d 20 44 75 64 61 2c 20 52 2e 20 4f 2e 2c 20 48 61 72 74 2c 20 50 2e 20 45 2e 2c 20 ..[2].Duda,.R..O.,.Hart,.P..E.,.
9b640 61 6e 64 20 53 74 6f 72 6b 2c 20 44 2e 20 47 2e 2c 20 22 50 61 74 74 65 72 6e 0a 20 20 20 20 20 and.Stork,.D..G.,."Pattern......
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9c1c0 a8 79 0a 80 01 00 00 00 90 7c 0a 80 01 00 00 00 28 75 0a 80 01 00 00 00 a8 7a 0a 80 01 00 00 00 .y.......|......(u.......z......
9c1e0 00 00 00 00 00 00 00 00 45 78 70 65 63 74 65 64 20 25 64 20 64 69 6d 65 6e 73 69 6f 6e 28 73 29 ........Expected.%d.dimension(s)
9c200 2c 20 67 6f 74 20 25 64 00 00 00 00 00 00 00 00 18 75 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 ,.got.%d.........u.......y......
9c220 00 00 00 00 00 00 00 00 42 75 66 66 65 72 20 64 74 79 70 65 20 6d 69 73 6d 61 74 63 68 2c 20 65 ........Buffer.dtype.mismatch,.e
9c240 78 70 65 63 74 65 64 20 25 73 25 73 25 73 20 62 75 74 20 67 6f 74 20 25 73 00 00 00 00 00 00 00 xpected.%s%s%s.but.got.%s.......
9c260 48 7b 0a 80 01 00 00 00 48 77 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 H{......Hw.......y..............
9c280 48 77 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 27 00 00 00 00 00 00 00 Hw.......y..............'.......
9c2a0 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 d0 cb 07 80 01 00 00 00 ................................
9c2c0 70 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 a0 5c 01 80 01 00 00 00 00 00 00 00 00 00 00 00 p................\..............
9c2e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c300 00 00 00 00 00 00 00 00 20 d3 07 80 01 00 00 00 58 ed 07 80 01 00 00 00 00 00 00 00 00 00 00 00 ................X...............
9c320 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 d0 59 01 80 01 00 00 00 00 00 00 00 00 00 00 00 .................Y..............
9c340 50 24 08 80 01 00 00 00 00 04 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 P$..............................
9c360 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c380 00 00 00 00 00 00 00 00 10 cf 09 80 01 00 00 00 00 00 00 00 00 00 00 00 00 6d 08 80 01 00 00 00 .........................m......
9c3a0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c3c0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 40 5e 01 80 01 00 00 00 ........................@^......
9c3e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c400 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c420 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 65 6e 64 00 00 00 00 00 ........................end.....
9c440 18 75 0a 80 01 00 00 00 18 7f 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 .u...............y..............
9c460 60 7f 0a 80 01 00 00 00 90 7d 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 80 74 0a 80 01 00 00 00 `........}.......y.......t......
9c480 48 75 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 70 78 0a 80 01 00 00 00 28 7e 0a 80 01 00 00 00 Hu..............px......(~......
9c4a0 c8 7f 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 65 6e 64 00 00 00 00 00 .........y..............end.....
9c4c0 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 f0 cc 07 80 01 00 00 00 ................................
9c4e0 a8 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 b0 55 01 80 01 00 00 00 00 00 00 00 00 00 00 00 .................U..............
9c500 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 c0 c7 01 80 01 00 00 00 ................................
9c520 00 00 00 00 00 00 00 00 f0 b7 08 80 01 00 00 00 c8 cd 07 80 01 00 00 00 00 00 00 00 00 00 00 00 ................................
9c540 00 00 00 00 00 00 00 00 c0 c5 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c560 50 6d 08 80 01 00 00 00 00 44 04 00 00 00 00 00 00 00 00 00 00 00 00 00 30 55 01 80 01 00 00 00 Pm.......D..............0U......
9c580 70 54 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 pT..............................
9c5a0 00 00 00 00 00 00 00 00 30 77 09 80 01 00 00 00 00 00 00 00 00 00 00 00 40 5d 08 80 01 00 00 00 ........0w..............@]......
9c5c0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c5e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 40 57 01 80 01 00 00 00 ........................@W......
9c600 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c620 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c640 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 27 63 6f 6d 70 6c 65 78 ........................'complex
9c660 20 6c 6f 6e 67 20 64 6f 75 62 6c 65 27 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .long.double'...................
9c680 00 00 00 00 00 00 00 00 d0 c4 07 80 01 00 00 00 d0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c6a0 b0 60 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .`..............................
9c6c0 00 00 00 00 00 00 00 00 00 e0 04 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c6e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 60 dd 04 80 01 00 00 00 ........................`.......
9c700 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 44 04 00 00 00 00 00 .........................D......
9c720 10 c5 07 80 01 00 00 00 50 60 01 80 01 00 00 00 d0 5f 01 80 01 00 00 00 00 00 00 00 00 00 00 00 ........P`......._..............
9c740 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 70 1e 08 80 01 00 00 00 ........................p.......
9c760 00 00 00 00 00 00 00 00 c0 11 08 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c780 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 f0 e1 04 80 01 00 00 00 ................................
9c7a0 00 00 00 00 00 00 00 00 50 61 01 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ........Pa......................
9c7c0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c7e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c800 00 00 00 00 00 00 00 00 27 63 6f 6d 70 6c 65 78 20 64 6f 75 62 6c 65 27 00 00 00 00 00 00 00 00 ........'complex.double'........
9c820 e8 7b 0a 80 01 00 00 00 28 77 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 .{......(w.......y..............
9c840 50 c1 07 80 01 00 00 00 f0 2f 02 80 01 00 00 00 03 00 00 00 00 00 00 00 a0 de 08 80 01 00 00 00 P......../......................
9c860 48 7b 0a 80 01 00 00 00 48 77 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 H{......Hw.......y..............
9c880 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c8a0 00 00 00 00 00 00 00 00 b8 cd 07 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9c8c0 90 7e 0a 80 01 00 00 00 38 1e 08 80 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .~......8.......................
9c8e0 00 00 00 00 00 00 00 00 27 66 6c 6f 61 74 27 00 80 7f 0a 80 01 00 00 00 48 77 0a 80 01 00 00 00 ........'float'.........Hw......
9c900 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 88 7b 0a 80 01 00 00 00 48 76 0a 80 01 00 00 00 .y...............{......Hv......
9c920 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 e8 7b 0a 80 01 00 00 00 50 7a 0a 80 01 00 00 00 .y...............{......Pz......
9c940 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 e8 78 0a 80 01 00 00 00 88 7d 0a 80 01 00 00 00 .y...............x.......}......
9c960 08 78 0a 80 01 00 00 00 b0 80 0a 80 01 00 00 00 e8 7d 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 .x...............}..............
9c980 e8 7b 0a 80 01 00 00 00 50 7a 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 .{......Pz.......y..............
9c9a0 e8 78 0a 80 01 00 00 00 48 77 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 .x......Hw.......y..............
9c9c0 60 7f 0a 80 01 00 00 00 90 7d 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 `........}.......y..............
9c9e0 70 77 0a 80 01 00 00 00 e8 75 0a 80 01 00 00 00 c8 79 0a 80 01 00 00 00 00 00 00 00 00 00 00 00 pw.......u.......y..............
9ca00 08 7c 0a 80 01 00 00 00 90 7b 0a 80 01 00 00 00 18 7f 0a 80 01 00 00 00 a8 79 0a 80 01 00 00 00 .|.......{...............y......
9ca20 00 00 00 00 00 00 00 00 27 75 6e 73 69 67 6e 65 64 20 6c 6f 6e 67 20 6c 6f 6e 67 27 00 00 00 00 ........'unsigned.long.long'....
9ca40 d0 80 0a 80 01 00 00 00 3c 6e 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ........<n......................
9ca60 01 00 00 00 00 00 00 00 e0 7a 0a 80 01 00 00 00 18 d0 06 80 01 00 00 00 08 00 00 00 00 00 00 00 .........z......................
9ca80 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 78 75 0a 80 01 00 00 00 c0 47 06 80 01 00 00 00 ................xu.......G......
9caa0 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 80 75 0a 80 01 00 00 00 .........................u......
9cac0 1c 7d 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 .}..............................
9cae0 08 7d 0a 80 01 00 00 00 ec cc 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}..............................
9cb00 00 01 01 00 00 00 00 00 20 78 0a 80 01 00 00 00 70 a6 06 80 01 00 00 00 33 00 00 00 00 00 00 00 .........x......p.......3.......
9cb20 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 c0 7a 0a 80 01 00 00 00 08 3c 07 80 01 00 00 00 .................z.......<......
9cb40 24 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 20 75 0a 80 01 00 00 00 $........................u......
9cb60 80 99 06 80 01 00 00 00 37 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 ........7.......................
9cb80 68 79 0a 80 01 00 00 00 68 7d 05 80 01 00 00 00 26 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 hy......h}......&...............
9cba0 00 01 00 00 00 00 00 00 40 76 0a 80 01 00 00 00 60 47 06 80 01 00 00 00 3d 00 00 00 00 00 00 00 ........@v......`G......=.......
9cbc0 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 08 77 0a 80 01 00 00 00 d0 1a 06 80 01 00 00 00 .................w..............
9cbe0 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 10 7f 0a 80 01 00 00 00 ................................
9cc00 50 03 07 80 01 00 00 00 42 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 P.......B.......................
9cc20 b8 7e 0a 80 01 00 00 00 70 8f 06 80 01 00 00 00 09 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .~......p.......................
9cc40 01 00 00 00 00 00 00 00 00 7c 0a 80 01 00 00 00 e0 3b 07 80 01 00 00 00 09 00 00 00 00 00 00 00 .........|.......;..............
9cc60 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 f0 7b 0a 80 01 00 00 00 a8 b1 05 80 01 00 00 00 .................{..............
9cc80 23 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 38 76 0a 80 01 00 00 00 #.......................8v......
9cca0 38 7d 05 80 01 00 00 00 26 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 8}......&.......................
9ccc0 98 77 0a 80 01 00 00 00 00 ad 06 80 01 00 00 00 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .w..............................
9cce0 00 01 01 00 00 00 00 00 d0 79 0a 80 01 00 00 00 f8 b0 05 80 01 00 00 00 1f 00 00 00 00 00 00 00 .........y......................
9cd00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 f8 78 0a 80 01 00 00 00 a8 15 06 80 01 00 00 00 .................x..............
9cd20 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 f8 74 0a 80 01 00 00 00 .........................t......
9cd40 e8 20 06 80 01 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ................................
9cd60 70 75 0a 80 01 00 00 00 98 c1 05 80 01 00 00 00 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 pu..............................
9cd80 01 00 00 00 00 00 00 00 90 78 0a 80 01 00 00 00 90 cf 06 80 01 00 00 00 20 00 00 00 00 00 00 00 .........x......................
9cda0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 f0 75 0a 80 01 00 00 00 88 48 05 80 01 00 00 00 .................u.......H......
9cdc0 18 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 80 7e 0a 80 01 00 00 00 .........................~......
9cde0 70 cf 06 80 01 00 00 00 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 p...............................
9ce00 d0 77 0a 80 01 00 00 00 88 15 06 80 01 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .w..............................
9ce20 01 00 00 00 00 00 00 00 50 7e 0a 80 01 00 00 00 78 6a 05 80 01 00 00 00 1d 00 00 00 00 00 00 00 ........P~......xj..............
9ce40 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 d8 80 0a 80 01 00 00 00 e0 f4 05 80 01 00 00 00 ................................
9ce60 25 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 40 7a 0a 80 01 00 00 00 %.......................@z......
9ce80 20 7b 05 80 01 00 00 00 1e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 .{..............................
9cea0 e0 7b 0a 80 01 00 00 00 e0 e7 05 80 01 00 00 00 1e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .{..............................
9cec0 01 00 00 00 00 00 00 00 c0 75 0a 80 01 00 00 00 40 b3 05 80 01 00 00 00 1f 00 00 00 00 00 00 00 .........u......@...............
9cee0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 20 7f 0a 80 01 00 00 00 38 e6 06 80 01 00 00 00 ........................8.......
9cf00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 58 76 0a 80 01 00 00 00 ........................Xv......
9cf20 20 7c 05 80 01 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 .|..............................
9cf40 e8 7c 0a 80 01 00 00 00 18 2a 06 80 01 00 00 00 22 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .|.......*......"...............
9cf60 01 00 00 00 00 00 00 00 e0 7d 0a 80 01 00 00 00 28 a6 06 80 01 00 00 00 32 00 00 00 00 00 00 00 .........}......(.......2.......
9cf80 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 98 7f 0a 80 01 00 00 00 e8 7c 05 80 01 00 00 00 .........................|......
9cfa0 2a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 b8 77 0a 80 01 00 00 00 *........................w......
9cfc0 20 ee 06 80 01 00 00 00 28 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ........(.......................
9cfe0 b0 7d 0a 80 01 00 00 00 18 cd 05 80 01 00 00 00 2b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}..............+...............
9d000 01 00 00 00 00 00 00 00 68 78 0a 80 01 00 00 00 48 cd 05 80 01 00 00 00 23 00 00 00 00 00 00 00 ........hx......H.......#.......
9d020 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 81 0a 80 01 00 00 00 98 7c 05 80 01 00 00 00 .........................|......
9d040 1d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 e0 74 0a 80 01 00 00 00 .........................t......
9d060 48 1b 06 80 01 00 00 00 1d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 H...............................
9d080 88 76 0a 80 01 00 00 00 a0 a5 06 80 01 00 00 00 22 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .v.............."...............
9d0a0 01 00 00 00 00 00 00 00 70 76 0a 80 01 00 00 00 80 b1 05 80 01 00 00 00 1f 00 00 00 00 00 00 00 ........pv......................
9d0c0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 a8 77 0a 80 01 00 00 00 88 c3 06 80 01 00 00 00 .................w..............
9d0e0 1e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 d8 7a 0a 80 01 00 00 00 .........................z......
9d100 20 15 06 80 01 00 00 00 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ................................
9d120 98 80 0a 80 01 00 00 00 68 e6 06 80 01 00 00 00 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ........h.......................
9d140 01 00 00 00 00 00 00 00 b8 7b 0a 80 01 00 00 00 d8 8e 06 80 01 00 00 00 1f 00 00 00 00 00 00 00 .........{......................
9d160 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 30 81 0a 80 01 00 00 00 d0 03 07 80 01 00 00 00 ................0...............
9d180 1e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 68 7a 0a 80 01 00 00 00 ........................hz......
9d1a0 c8 6e 06 80 01 00 00 00 26 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 .n......&.......................
9d1c0 48 79 0a 80 01 00 00 00 c8 48 05 80 01 00 00 00 2a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 Hy.......H......*...............
9d1e0 01 00 00 00 00 00 00 00 b8 7d 0a 80 01 00 00 00 e0 ad 06 80 01 00 00 00 25 00 00 00 00 00 00 00 .........}..............%.......
9d200 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 10 7c 0a 80 01 00 00 00 40 7c 05 80 01 00 00 00 .................|......@|......
9d220 25 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 98 79 0a 80 01 00 00 00 %........................y......
9d240 00 b3 05 80 01 00 00 00 21 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ........!.......................
9d260 40 7c 0a 80 01 00 00 00 40 16 06 80 01 00 00 00 21 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 @|......@.......!...............
9d280 01 00 00 00 00 00 00 00 70 7d 0a 80 01 00 00 00 20 b9 06 80 01 00 00 00 1d 00 00 00 00 00 00 00 ........p}......................
9d2a0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 08 7e 0a 80 01 00 00 00 d0 ed 06 80 01 00 00 00 .................~..............
9d2c0 1f 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 60 7c 0a 80 01 00 00 00 ........................`|......
9d2e0 18 04 07 80 01 00 00 00 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ................................
9d300 c8 7a 0a 80 01 00 00 00 40 2a 06 80 01 00 00 00 1e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .z......@*......................
9d320 01 00 00 00 00 00 00 00 b0 75 0a 80 01 00 00 00 70 cd 05 80 01 00 00 00 1b 00 00 00 00 00 00 00 .........u......p...............
9d340 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 c0 76 0a 80 01 00 00 00 48 a7 05 80 01 00 00 00 .................v......H.......
9d360 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 48 7d 0a 80 01 00 00 00 ........................H}......
9d380 10 ef 06 80 01 00 00 00 4c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 ........L.......................
9d3a0 48 74 0a 80 01 00 00 00 08 6e 06 80 01 00 00 00 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 Ht.......n......................
9d3c0 00 01 01 00 00 00 00 00 78 78 0a 80 01 00 00 00 70 7c 05 80 01 00 00 00 22 00 00 00 00 00 00 00 ........xx......p|......".......
9d3e0 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 e0 7c 0a 80 01 00 00 00 30 b2 05 80 01 00 00 00 .................|......0.......
9d400 5b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 7a 0a 80 01 00 00 00 [........................z......
9d420 c8 15 06 80 01 00 00 00 3f 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ........?.......................
9d440 50 76 0a 80 01 00 00 00 d0 ee 06 80 01 00 00 00 30 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 Pv..............0...............
9d460 00 01 00 00 00 00 00 00 90 76 0a 80 01 00 00 00 10 cf 06 80 01 00 00 00 1e 00 00 00 00 00 00 00 .........v......................
9d480 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 48 7f 0a 80 01 00 00 00 9c b0 05 80 01 00 00 00 ................H...............
9d4a0 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 a8 80 0a 80 01 00 00 00 ................................
9d4c0 b8 99 06 80 01 00 00 00 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9d4e0 a0 77 0a 80 01 00 00 00 08 a6 06 80 01 00 00 00 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .w..............................
9d500 00 01 00 00 00 00 00 00 f8 7c 0a 80 01 00 00 00 c0 f4 05 80 01 00 00 00 1a 00 00 00 00 00 00 00 .........|......................
9d520 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 f8 75 0a 80 01 00 00 00 98 d5 05 80 01 00 00 00 .................u..............
9d540 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 a8 7c 0a 80 01 00 00 00 .........................|......
9d560 b8 ed 06 80 01 00 00 00 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9d580 78 7d 0a 80 01 00 00 00 94 7c 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 x}.......|......................
9d5a0 00 00 01 00 00 00 00 00 38 7d 0a 80 01 00 00 00 d0 2a 06 80 01 00 00 00 29 00 00 00 00 00 00 00 ........8}.......*......).......
9d5c0 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 20 80 0a 80 01 00 00 00 a0 03 07 80 01 00 00 00 ................................
9d5e0 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 28 76 0a 80 01 00 00 00 ........................(v......
9d600 e0 cf 06 80 01 00 00 00 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9d620 00 7d 0a 80 01 00 00 00 5c d0 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}......\.......................
9d640 00 01 01 00 00 00 00 00 78 76 0a 80 01 00 00 00 10 b9 06 80 01 00 00 00 0c 00 00 00 00 00 00 00 ........xv......................
9d660 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 d8 7c 0a 80 01 00 00 00 20 0d 07 80 01 00 00 00 .................|..............
9d680 8c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 60 80 0a 80 01 00 00 00 ........................`.......
9d6a0 30 3c 07 80 01 00 00 00 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 0<..............................
9d6c0 40 81 0a 80 01 00 00 00 b0 55 05 80 01 00 00 00 0f 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 @........U......................
9d6e0 00 01 01 00 00 00 00 00 28 7d 0a 80 01 00 00 00 a8 b2 05 80 01 00 00 00 09 00 00 00 00 00 00 00 ........(}......................
9d700 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 10 7a 0a 80 01 00 00 00 f4 b0 05 80 01 00 00 00 .................z..............
9d720 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 28 78 0a 80 01 00 00 00 ........................(x......
9d740 58 e6 06 80 01 00 00 00 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 X...............................
9d760 f0 79 0a 80 01 00 00 00 a0 b0 05 80 01 00 00 00 21 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .y..............!...............
9d780 00 01 00 00 00 00 00 00 58 7c 0a 80 01 00 00 00 40 48 05 80 01 00 00 00 22 00 00 00 00 00 00 00 ........X|......@H......".......
9d7a0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 58 7d 0a 80 01 00 00 00 88 1b 06 80 01 00 00 00 ................X}..............
9d7c0 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 20 7e 0a 80 01 00 00 00 .........................~......
9d7e0 f0 ed 06 80 01 00 00 00 2e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ................................
9d800 10 7e 0a 80 01 00 00 00 30 cf 06 80 01 00 00 00 29 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .~......0.......)...............
9d820 01 00 00 00 00 00 00 00 98 75 0a 80 01 00 00 00 50 3c 07 80 01 00 00 00 28 00 00 00 00 00 00 00 .........u......P<......(.......
9d840 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 38 7e 0a 80 01 00 00 00 c0 1a 06 80 01 00 00 00 ................8~..............
9d860 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 f8 77 0a 80 01 00 00 00 .........................w......
9d880 58 e8 05 80 01 00 00 00 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 X...............................
9d8a0 d8 74 0a 80 01 00 00 00 78 f4 05 80 01 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .t......x.......................
9d8c0 00 01 01 00 00 00 00 00 40 7b 0a 80 01 00 00 00 50 15 06 80 01 00 00 00 37 00 00 00 00 00 00 00 ........@{......P.......7.......
9d8e0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 a0 75 0a 80 01 00 00 00 10 8f 06 80 01 00 00 00 .................u..............
9d900 46 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 30 79 0a 80 01 00 00 00 F.......................0y......
9d920 c4 48 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 .H..............................
9d940 b8 7f 0a 80 01 00 00 00 14 cd 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9d960 01 00 00 00 00 00 00 00 a0 76 0a 80 01 00 00 00 f4 b4 05 80 01 00 00 00 02 00 00 00 00 00 00 00 .........v......................
9d980 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 60 78 0a 80 01 00 00 00 62 48 05 80 01 00 00 00 ................`x......bH......
9d9a0 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 78 74 0a 80 01 00 00 00 ........................xt......
9d9c0 fc 48 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 .H..............................
9d9e0 60 81 0a 80 01 00 00 00 fc 48 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 `........H......................
9da00 01 00 01 00 00 00 00 00 b0 76 0a 80 01 00 00 00 b8 ac 06 80 01 00 00 00 1c 00 00 00 00 00 00 00 .........v......................
9da20 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 60 77 0a 80 01 00 00 00 f8 b4 05 80 01 00 00 00 ................`w..............
9da40 2e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 18 7c 0a 80 01 00 00 00 .........................|......
9da60 b8 c1 05 80 01 00 00 00 39 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ........9.......................
9da80 20 7c 0a 80 01 00 00 00 b0 cf 06 80 01 00 00 00 29 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .|..............)...............
9daa0 01 00 00 00 00 00 00 00 c0 80 0a 80 01 00 00 00 b4 48 05 80 01 00 00 00 04 00 00 00 00 00 00 00 .................H..............
9dac0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 b0 7c 0a 80 01 00 00 00 34 7d 05 80 01 00 00 00 .................|......4}......
9dae0 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 50 81 0a 80 01 00 00 00 ........................P.......
9db00 08 1b 06 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9db20 e8 7d 0a 80 01 00 00 00 08 c2 05 80 01 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}..............................
9db40 00 01 01 00 00 00 00 00 50 80 0a 80 01 00 00 00 64 b0 05 80 01 00 00 00 06 00 00 00 00 00 00 00 ........P.......d...............
9db60 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 d8 76 0a 80 01 00 00 00 00 e8 05 80 01 00 00 00 .................v..............
9db80 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 70 79 0a 80 01 00 00 00 ........................py......
9dba0 8c b2 05 80 01 00 00 00 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9dbc0 28 81 0a 80 01 00 00 00 fc c1 05 80 01 00 00 00 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 (...............................
9dbe0 00 01 01 00 00 00 00 00 c8 7b 0a 80 01 00 00 00 cc e7 05 80 01 00 00 00 06 00 00 00 00 00 00 00 .........{......................
9dc00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 38 7a 0a 80 01 00 00 00 38 b3 05 80 01 00 00 00 ................8z......8.......
9dc20 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 d8 7f 0a 80 01 00 00 00 ................................
9dc40 68 b9 06 80 01 00 00 00 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 h...............................
9dc60 68 80 0a 80 01 00 00 00 1c 6b 05 80 01 00 00 00 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 h........k......................
9dc80 00 01 01 00 00 00 00 00 50 7c 0a 80 01 00 00 00 d0 99 06 80 01 00 00 00 ca 00 00 00 00 00 00 00 ........P|......................
9dca0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 a8 78 0a 80 01 00 00 00 78 48 05 80 01 00 00 00 .................x......xH......
9dcc0 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 80 79 0a 80 01 00 00 00 .........................y......
9dce0 34 8c 05 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 4...............................
9dd00 78 7f 0a 80 01 00 00 00 4c 47 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 x.......LG......................
9dd20 00 01 01 00 00 00 00 00 f8 7b 0a 80 01 00 00 00 dc cc 05 80 01 00 00 00 02 00 00 00 00 00 00 00 .........{......................
9dd40 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 d0 7d 0a 80 01 00 00 00 dc cc 05 80 01 00 00 00 .................}..............
9dd60 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 88 79 0a 80 01 00 00 00 .........................y......
9dd80 78 3c 07 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 x<..............................
9dda0 20 7b 0a 80 01 00 00 00 40 8c 05 80 01 00 00 00 07 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .{......@.......................
9ddc0 01 00 00 00 00 00 00 00 78 80 0a 80 01 00 00 00 70 b1 05 80 01 00 00 00 0e 00 00 00 00 00 00 00 ........x.......p...............
9dde0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 d0 76 0a 80 01 00 00 00 70 b1 05 80 01 00 00 00 .................v......p.......
9de00 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 a0 7d 0a 80 01 00 00 00 .........................}......
9de20 f8 8e 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9de40 68 77 0a 80 01 00 00 00 68 e8 05 80 01 00 00 00 29 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 hw......h.......)...............
9de60 01 00 00 00 00 00 00 00 68 81 0a 80 01 00 00 00 60 b3 05 80 01 00 00 00 80 01 00 00 00 00 00 00 ........h.......`...............
9de80 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 e0 75 0a 80 01 00 00 00 54 7b 05 80 01 00 00 00 .................u......T{......
9dea0 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 50 77 0a 80 01 00 00 00 ........................Pw......
9dec0 54 7b 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 T{..............................
9dee0 88 7a 0a 80 01 00 00 00 40 15 06 80 01 00 00 00 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .z......@.......................
9df00 00 01 01 00 00 00 00 00 b8 78 0a 80 01 00 00 00 40 15 06 80 01 00 00 00 08 00 00 00 00 00 00 00 .........x......@...............
9df20 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 50 7f 0a 80 01 00 00 00 78 1b 06 80 01 00 00 00 ................P.......x.......
9df40 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 90 7c 0a 80 01 00 00 00 .........................|......
9df60 08 cd 05 80 01 00 00 00 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9df80 00 79 0a 80 01 00 00 00 a8 c3 06 80 01 00 00 00 34 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .y..............4...............
9dfa0 01 00 00 00 00 00 00 00 c8 78 0a 80 01 00 00 00 90 cd 05 80 01 00 00 00 06 08 00 00 00 00 00 00 .........x......................
9dfc0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 b0 79 0a 80 01 00 00 00 20 6c 05 80 01 00 00 00 .................y.......l......
9dfe0 f6 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 10 76 0a 80 01 00 00 00 .........................v......
9e000 a0 48 05 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 .H..............................
9e020 08 7b 0a 80 01 00 00 00 a0 48 05 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .{.......H......................
9e040 01 00 01 00 00 00 00 00 38 7b 0a 80 01 00 00 00 08 04 07 80 01 00 00 00 0a 00 00 00 00 00 00 00 ........8{......................
9e060 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 30 7b 0a 80 01 00 00 00 a8 6a 05 80 01 00 00 00 ................0{.......j......
9e080 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 68 74 0a 80 01 00 00 00 ........................ht......
9e0a0 98 6a 05 80 01 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 .j..............................
9e0c0 e0 79 0a 80 01 00 00 00 c4 6a 05 80 01 00 00 00 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .y.......j......................
9e0e0 00 01 01 00 00 00 00 00 50 78 0a 80 01 00 00 00 d0 b1 05 80 01 00 00 00 54 00 00 00 00 00 00 00 ........Px..............T.......
9e100 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 48 7a 0a 80 01 00 00 00 78 b0 05 80 01 00 00 00 ................Hz......x.......
9e120 18 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 50 75 0a 80 01 00 00 00 ........................Pu......
9e140 b8 7c 05 80 01 00 00 00 1a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 .|..............................
9e160 e8 79 0a 80 01 00 00 00 40 ad 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .y......@.......................
9e180 00 01 01 00 00 00 00 00 88 7c 0a 80 01 00 00 00 f4 b2 05 80 01 00 00 00 07 00 00 00 00 00 00 00 .........|......................
9e1a0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 08 80 0a 80 01 00 00 00 bc 6a 05 80 01 00 00 00 .........................j......
9e1c0 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 20 7d 0a 80 01 00 00 00 .........................}......
9e1e0 c8 8e 06 80 01 00 00 00 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9e200 c8 74 0a 80 01 00 00 00 d4 7c 05 80 01 00 00 00 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .t.......|......................
9e220 00 01 01 00 00 00 00 00 68 75 0a 80 01 00 00 00 78 ee 06 80 01 00 00 00 25 00 00 00 00 00 00 00 ........hu......x.......%.......
9e240 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 48 81 0a 80 01 00 00 00 20 47 06 80 01 00 00 00 ................H........G......
9e260 29 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 b8 7a 0a 80 01 00 00 00 )........................z......
9e280 d4 cc 05 80 01 00 00 00 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9e2a0 00 75 0a 80 01 00 00 00 98 b9 06 80 01 00 00 00 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .u..............................
9e2c0 00 01 01 00 00 00 00 00 28 7c 0a 80 01 00 00 00 28 6b 05 80 01 00 00 00 18 00 00 00 00 00 00 00 ........(|......(k..............
9e2e0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 18 75 0a 80 01 00 00 00 44 a7 05 80 01 00 00 00 .................u......D.......
9e300 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 48 78 0a 80 01 00 00 00 ........................Hx......
9e320 44 a7 05 80 01 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 D...............................
9e340 90 7b 0a 80 01 00 00 00 b4 b2 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .{..............................
9e360 00 01 01 00 00 00 00 00 90 7f 0a 80 01 00 00 00 b4 b2 05 80 01 00 00 00 06 00 00 00 00 00 00 00 ................................
9e380 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 08 7c 0a 80 01 00 00 00 fc 3b 07 80 01 00 00 00 .................|.......;......
9e3a0 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 80 76 0a 80 01 00 00 00 .........................v......
9e3c0 fc 3b 07 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 .;..............................
9e3e0 e0 80 0a 80 01 00 00 00 e0 cc 05 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9e400 00 01 01 00 00 00 00 00 88 7f 0a 80 01 00 00 00 e0 c3 06 80 01 00 00 00 30 0b 00 00 00 00 00 00 ........................0.......
9e420 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 70 7a 0a 80 01 00 00 00 6c cd 05 80 01 00 00 00 ................pz......l.......
9e440 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 00 80 0a 80 01 00 00 00 ................................
9e460 6c 6a 05 80 01 00 00 00 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 lj..............................
9e480 80 74 0a 80 01 00 00 00 ec 3b 07 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .t.......;......................
9e4a0 00 01 01 00 00 00 00 00 c8 79 0a 80 01 00 00 00 18 1b 06 80 01 00 00 00 10 00 00 00 00 00 00 00 .........y......................
9e4c0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 b0 78 0a 80 01 00 00 00 24 b1 05 80 01 00 00 00 .................x......$.......
9e4e0 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 18 7b 0a 80 01 00 00 00 .........................{......
9e500 24 b1 05 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 $...............................
9e520 b8 80 0a 80 01 00 00 00 a4 b9 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9e540 00 01 01 00 00 00 00 00 f0 76 0a 80 01 00 00 00 90 b0 05 80 01 00 00 00 0b 00 00 00 00 00 00 00 .........v......................
9e560 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 10 78 0a 80 01 00 00 00 ec b0 05 80 01 00 00 00 .................x..............
9e580 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 48 75 0a 80 01 00 00 00 ........................Hu......
9e5a0 00 8f 06 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9e5c0 28 80 0a 80 01 00 00 00 18 b1 05 80 01 00 00 00 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 (...............................
9e5e0 00 01 01 00 00 00 00 00 f0 77 0a 80 01 00 00 00 c8 b2 05 80 01 00 00 00 0a 00 00 00 00 00 00 00 .........w......................
9e600 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 68 7c 0a 80 01 00 00 00 cc 6a 05 80 01 00 00 00 ................h|.......j......
9e620 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 10 79 0a 80 01 00 00 00 .........................y......
9e640 2c 16 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ,...............................
9e660 88 78 0a 80 01 00 00 00 44 5a 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .x......DZ......................
9e680 00 01 01 00 00 00 00 00 b0 7a 0a 80 01 00 00 00 a8 ee 06 80 01 00 00 00 09 00 00 00 00 00 00 00 .........z......................
9e6a0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 88 80 0a 80 01 00 00 00 f0 39 06 80 01 00 00 00 .........................9......
9e6c0 1e 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 10 75 0a 80 01 00 00 00 .........................u......
9e6e0 f4 ac 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9e700 e8 75 0a 80 01 00 00 00 58 ad 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .u......X.......................
9e720 00 01 01 00 00 00 00 00 70 7c 0a 80 01 00 00 00 a0 ee 06 80 01 00 00 00 08 00 00 00 00 00 00 00 ........p|......................
9e740 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 d0 7f 0a 80 01 00 00 00 a8 f4 05 80 01 00 00 00 ................................
9e760 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 08 78 0a 80 01 00 00 00 .........................x......
9e780 d4 e7 05 80 01 00 00 00 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9e7a0 a0 79 0a 80 01 00 00 00 00 49 05 80 01 00 00 00 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .y.......I......................
9e7c0 00 01 01 00 00 00 00 00 90 80 0a 80 01 00 00 00 00 49 05 80 01 00 00 00 08 00 00 00 00 00 00 00 .................I..............
9e7e0 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 38 78 0a 80 01 00 00 00 c4 50 06 80 01 00 00 00 ................8x.......P......
9e800 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 18 7a 0a 80 01 00 00 00 .........................z......
9e820 10 0a 06 80 01 00 00 00 09 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ................................
9e840 f8 76 0a 80 01 00 00 00 80 b9 06 80 01 00 00 00 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .v..............................
9e860 00 01 01 00 00 00 00 00 38 79 0a 80 01 00 00 00 c0 55 05 80 01 00 00 00 0f 00 00 00 00 00 00 00 ........8y.......U..............
9e880 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 c8 77 0a 80 01 00 00 00 c0 7b 06 80 01 00 00 00 .................w.......{......
9e8a0 4b 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 38 7f 0a 80 01 00 00 00 K.......................8.......
9e8c0 48 ad 06 80 01 00 00 00 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 H...............................
9e8e0 08 76 0a 80 01 00 00 00 a8 ad 06 80 01 00 00 00 36 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .v..............6...............
9e900 00 01 00 00 00 00 00 00 30 75 0a 80 01 00 00 00 60 ad 06 80 01 00 00 00 08 00 00 00 00 00 00 00 ........0u......`...............
9e920 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 80 7a 0a 80 01 00 00 00 a0 d5 05 80 01 00 00 00 .................z..............
9e940 29 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 08 75 0a 80 01 00 00 00 )........................u......
9e960 e0 b0 05 80 01 00 00 00 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9e980 90 7d 0a 80 01 00 00 00 18 c2 05 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}..............................
9e9a0 00 01 01 00 00 00 00 00 30 7a 0a 80 01 00 00 00 f8 a6 06 80 01 00 00 00 0b 00 00 00 00 00 00 00 ........0z......................
9e9c0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 d8 7b 0a 80 01 00 00 00 90 7b 05 80 01 00 00 00 .................{.......{......
9e9e0 26 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 38 7c 0a 80 01 00 00 00 &.......................8|......
9ea00 80 3c 07 80 01 00 00 00 9f 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 .<..............................
9ea20 00 7f 0a 80 01 00 00 00 fc cc 05 80 01 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9ea40 00 01 01 00 00 00 00 00 10 7d 0a 80 01 00 00 00 4c 7b 05 80 01 00 00 00 07 00 00 00 00 00 00 00 .........}......L{..............
9ea60 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 b0 7b 0a 80 01 00 00 00 08 d0 06 80 01 00 00 00 .................{..............
9ea80 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 50 79 0a 80 01 00 00 00 ........................Py......
9eaa0 b8 1b 06 80 01 00 00 00 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9eac0 f8 79 0a 80 01 00 00 00 d4 ac 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .y..............................
9eae0 00 01 01 00 00 00 00 00 40 74 0a 80 01 00 00 00 80 1b 06 80 01 00 00 00 06 00 00 00 00 00 00 00 ........@t......................
9eb00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 e8 80 0a 80 01 00 00 00 d4 47 06 80 01 00 00 00 .........................G......
9eb20 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 08 81 0a 80 01 00 00 00 ................................
9eb40 24 b3 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 $...............................
9eb60 b0 7e 0a 80 01 00 00 00 64 8f 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .~......d.......................
9eb80 00 01 01 00 00 00 00 00 30 74 0a 80 01 00 00 00 08 21 06 80 01 00 00 00 09 00 00 00 00 00 00 00 ........0t.......!..............
9eba0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 00 7e 0a 80 01 00 00 00 b0 0d 07 80 01 00 00 00 .................~..............
9ebc0 d4 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 78 77 0a 80 01 00 00 00 ........................xw......
9ebe0 c8 03 07 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9ec00 10 80 0a 80 01 00 00 00 58 6e 06 80 01 00 00 00 38 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ........Xn......8...............
9ec20 01 00 00 00 00 00 00 00 50 74 0a 80 01 00 00 00 88 2a 06 80 01 00 00 00 09 00 00 00 00 00 00 00 ........Pt.......*..............
9ec40 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 78 7a 0a 80 01 00 00 00 2c b1 05 80 01 00 00 00 ................xz......,.......
9ec60 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 38 81 0a 80 01 00 00 00 ........................8.......
9ec80 e0 b4 05 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9eca0 10 77 0a 80 01 00 00 00 b8 6e 06 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .w.......n......................
9ecc0 00 01 01 00 00 00 00 00 18 78 0a 80 01 00 00 00 f0 03 07 80 01 00 00 00 0b 00 00 00 00 00 00 00 .........x......................
9ece0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 a8 7b 0a 80 01 00 00 00 08 ae 06 80 01 00 00 00 .................{..............
9ed00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 88 7d 0a 80 01 00 00 00 .........................}......
9ed20 10 ad 06 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9ed40 40 78 0a 80 01 00 00 00 98 ac 06 80 01 00 00 00 1f 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 @x..............................
9ed60 00 01 00 00 00 00 00 00 48 76 0a 80 01 00 00 00 54 a7 05 80 01 00 00 00 06 00 00 00 00 00 00 00 ........Hv......T...............
9ed80 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 20 76 0a 80 01 00 00 00 54 a7 05 80 01 00 00 00 .................v......T.......
9eda0 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 80 78 0a 80 01 00 00 00 .........................x......
9edc0 d4 b0 05 80 01 00 00 00 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9ede0 10 7b 0a 80 01 00 00 00 d4 b0 05 80 01 00 00 00 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .{..............................
9ee00 01 00 01 00 00 00 00 00 08 7f 0a 80 01 00 00 00 10 82 06 80 01 00 00 00 a5 0c 00 00 00 00 00 00 ................................
9ee20 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 80 80 0a 80 01 00 00 00 84 1a 07 80 01 00 00 00 ................................
9ee40 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 e8 7a 0a 80 01 00 00 00 .........................z......
9ee60 40 6b 05 80 01 00 00 00 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 @k..............................
9ee80 58 79 0a 80 01 00 00 00 48 ee 06 80 01 00 00 00 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 Xy......H.......................
9eea0 01 00 00 00 00 00 00 00 20 79 0a 80 01 00 00 00 48 9a 05 80 01 00 00 00 05 00 00 00 00 00 00 00 .........y......H...............
9eec0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 00 7b 0a 80 01 00 00 00 68 1b 06 80 01 00 00 00 .................{......h.......
9eee0 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 48 7b 0a 80 01 00 00 00 ........................H{......
9ef00 e4 7c 05 80 01 00 00 00 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 .|..............................
9ef20 70 7e 0a 80 01 00 00 00 e4 7c 05 80 01 00 00 00 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 p~.......|......................
9ef40 01 00 01 00 00 00 00 00 68 7f 0a 80 01 00 00 00 94 2a 06 80 01 00 00 00 05 00 00 00 00 00 00 00 ........h........*..............
9ef60 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 30 7c 0a 80 01 00 00 00 d8 7c 05 80 01 00 00 00 ................0|.......|......
9ef80 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 68 76 0a 80 01 00 00 00 ........................hv......
9efa0 80 d0 06 80 01 00 00 00 64 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ........d.......................
9efc0 88 77 0a 80 01 00 00 00 90 1a 07 80 01 00 00 00 e9 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .w..............................
9efe0 01 00 00 00 00 00 00 00 18 79 0a 80 01 00 00 00 10 ae 06 80 01 00 00 00 ef 0a 00 00 00 00 00 00 .........y......................
9f000 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 60 7f 0a 80 01 00 00 00 84 48 05 80 01 00 00 00 ................`........H......
9f020 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 28 7a 0a 80 01 00 00 00 ........................(z......
9f040 50 b1 05 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 P...............................
9f060 28 7b 0a 80 01 00 00 00 40 7b 05 80 01 00 00 00 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ({......@{......................
9f080 01 00 01 00 00 00 00 00 60 7a 0a 80 01 00 00 00 38 5a 06 80 01 00 00 00 0b 00 00 00 00 00 00 00 ........`z......8Z..............
9f0a0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 80 77 0a 80 01 00 00 00 34 b3 05 80 01 00 00 00 .................w......4.......
9f0c0 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 d0 7c 0a 80 01 00 00 00 .........................|......
9f0e0 a0 6e 06 80 01 00 00 00 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 .n..............................
9f100 80 7f 0a 80 01 00 00 00 7c 2a 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ........|*......................
9f120 00 01 01 00 00 00 00 00 20 81 0a 80 01 00 00 00 7c 2a 06 80 01 00 00 00 05 00 00 00 00 00 00 00 ................|*..............
9f140 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 48 7c 0a 80 01 00 00 00 78 ad 06 80 01 00 00 00 ................H|......x.......
9f160 23 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 e0 76 0a 80 01 00 00 00 #........................v......
9f180 28 1b 06 80 01 00 00 00 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 (...............................
9f1a0 88 74 0a 80 01 00 00 00 40 b9 06 80 01 00 00 00 25 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .t......@.......%...............
9f1c0 01 00 00 00 00 00 00 00 90 79 0a 80 01 00 00 00 a0 b2 05 80 01 00 00 00 08 00 00 00 00 00 00 00 .........y......................
9f1e0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 a8 7a 0a 80 01 00 00 00 34 b1 05 80 01 00 00 00 .................z......4.......
9f200 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 70 7f 0a 80 01 00 00 00 ........................p.......
9f220 28 b5 05 80 01 00 00 00 27 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 (.......'.......................
9f240 b8 7c 0a 80 01 00 00 00 e8 6a 05 80 01 00 00 00 32 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .|.......j......2...............
9f260 01 00 00 00 00 00 00 00 b0 80 0a 80 01 00 00 00 48 15 06 80 01 00 00 00 05 00 00 00 00 00 00 00 ................H...............
9f280 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 30 78 0a 80 01 00 00 00 68 f4 05 80 01 00 00 00 ................0x......h.......
9f2a0 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 88 7b 0a 80 01 00 00 00 .........................{......
9f2c0 dc b2 05 80 01 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9f2e0 60 74 0a 80 01 00 00 00 dc b2 05 80 01 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 `t..............................
9f300 01 00 01 00 00 00 00 00 58 81 0a 80 01 00 00 00 d0 55 05 80 01 00 00 00 9a 14 00 00 00 00 00 00 ........X........U..............
9f320 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 98 7c 0a 80 01 00 00 00 c0 ef 06 80 01 00 00 00 .................|..............
9f340 90 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 40 7e 0a 80 01 00 00 00 ........................@~......
9f360 50 5a 06 80 01 00 00 00 b7 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 PZ..............................
9f380 e8 7b 0a 80 01 00 00 00 3c b1 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .{......<.......................
9f3a0 00 01 01 00 00 00 00 00 48 7e 0a 80 01 00 00 00 3c b1 05 80 01 00 00 00 02 00 00 00 00 00 00 00 ........H~......<...............
9f3c0 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 80 7c 0a 80 01 00 00 00 30 6e 06 80 01 00 00 00 .................|......0n......
9f3e0 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 50 7b 0a 80 01 00 00 00 ........................P{......
9f400 94 03 07 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9f420 28 7e 0a 80 01 00 00 00 dc ac 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 (~..............................
9f440 00 01 01 00 00 00 00 00 b0 7f 0a 80 01 00 00 00 dc ac 06 80 01 00 00 00 05 00 00 00 00 00 00 00 ................................
9f460 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 c8 80 0a 80 01 00 00 00 fc 03 07 80 01 00 00 00 ................................
9f480 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 58 80 0a 80 01 00 00 00 ........................X.......
9f4a0 50 b5 05 80 01 00 00 00 42 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 P.......B.......................
9f4c0 c0 7c 0a 80 01 00 00 00 08 f5 05 80 01 00 00 00 24 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .|..............$...............
9f4e0 01 00 00 00 00 00 00 00 f8 7e 0a 80 01 00 00 00 58 47 06 80 01 00 00 00 08 00 00 00 00 00 00 00 .........~......XG..............
9f500 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 70 78 0a 80 01 00 00 00 b4 47 06 80 01 00 00 00 ................px.......G......
9f520 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 98 74 0a 80 01 00 00 00 .........................t......
9f540 b4 47 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 .G..............................
9f560 f0 7e 0a 80 01 00 00 00 b8 2a 06 80 01 00 00 00 17 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .~.......*......................
9f580 01 00 00 00 00 00 00 00 f0 80 0a 80 01 00 00 00 88 ef 06 80 01 00 00 00 33 00 00 00 00 00 00 00 ........................3.......
9f5a0 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 18 7f 0a 80 01 00 00 00 64 16 06 80 01 00 00 00 ........................d.......
9f5c0 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 e0 7e 0a 80 01 00 00 00 .........................~......
9f5e0 64 16 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 d...............................
9f600 f0 7a 0a 80 01 00 00 00 20 c2 05 80 01 00 00 00 b2 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .z..............................
9f620 01 00 00 00 00 00 00 00 70 80 0a 80 01 00 00 00 70 49 05 80 01 00 00 00 3d 0c 00 00 00 00 00 00 ........p.......pI......=.......
9f640 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 38 75 0a 80 01 00 00 00 90 7d 05 80 01 00 00 00 ................8u.......}......
9f660 a4 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 d0 75 0a 80 01 00 00 00 .........................u......
9f680 68 d0 06 80 01 00 00 00 15 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 h...............................
9f6a0 58 75 0a 80 01 00 00 00 94 c1 05 80 01 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 Xu..............................
9f6c0 00 01 01 00 00 00 00 00 c8 7f 0a 80 01 00 00 00 68 7c 05 80 01 00 00 00 08 00 00 00 00 00 00 00 ................h|..............
9f6e0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 78 79 0a 80 01 00 00 00 68 7c 05 80 01 00 00 00 ................xy......h|......
9f700 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 10 81 0a 80 01 00 00 00 ................................
9f720 58 ee 06 80 01 00 00 00 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 X...............................
9f740 f8 80 0a 80 01 00 00 00 20 ad 06 80 01 00 00 00 1d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................................
9f760 01 00 00 00 00 00 00 00 30 77 0a 80 01 00 00 00 a8 a6 06 80 01 00 00 00 1b 00 00 00 00 00 00 00 ........0w......................
9f780 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 40 80 0a 80 01 00 00 00 f0 a5 06 80 01 00 00 00 ................@...............
9f7a0 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 a0 78 0a 80 01 00 00 00 .........................x......
9f7c0 60 7d 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 `}..............................
9f7e0 60 79 0a 80 01 00 00 00 f8 09 06 80 01 00 00 00 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 `y..............................
9f800 00 01 01 00 00 00 00 00 80 7b 0a 80 01 00 00 00 60 ef 06 80 01 00 00 00 27 00 00 00 00 00 00 00 .........{......`.......'.......
9f820 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 30 7f 0a 80 01 00 00 00 38 04 07 80 01 00 00 00 ................0.......8.......
9f840 22 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 c8 7e 0a 80 01 00 00 00 "........................~......
9f860 b0 f4 05 80 01 00 00 00 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9f880 98 7d 0a 80 01 00 00 00 f0 1a 06 80 01 00 00 00 18 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}..............................
9f8a0 00 01 01 00 00 00 00 00 70 77 0a 80 01 00 00 00 fc b2 05 80 01 00 00 00 04 00 00 00 00 00 00 00 ........pw......................
9f8c0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 c0 7b 0a 80 01 00 00 00 50 6b 05 80 01 00 00 00 .................{......Pk......
9f8e0 c2 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 f0 78 0a 80 01 00 00 00 .........................x......
9f900 68 ad 06 80 01 00 00 00 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 h...............................
9f920 a0 7b 0a 80 01 00 00 00 c4 1b 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .{..............................
9f940 00 01 01 00 00 00 00 00 d8 79 0a 80 01 00 00 00 b4 c1 05 80 01 00 00 00 04 00 00 00 00 00 00 00 .........y......................
9f960 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 a0 7f 0a 80 01 00 00 00 88 f4 05 80 01 00 00 00 ................................
9f980 1a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 b8 74 0a 80 01 00 00 00 .........................t......
9f9a0 d0 a6 06 80 01 00 00 00 22 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ........".......................
9f9c0 50 7a 0a 80 01 00 00 00 6c b1 05 80 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 Pz......l.......................
9f9e0 00 01 01 00 00 00 00 00 d0 78 0a 80 01 00 00 00 6c b1 05 80 01 00 00 00 02 00 00 00 00 00 00 00 .........x......l...............
9fa00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 70 74 0a 80 01 00 00 00 18 6e 06 80 01 00 00 00 ................pt.......n......
9fa20 18 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 f0 74 0a 80 01 00 00 00 .........................t......
9fa40 cc 47 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 .G..............................
9fa60 18 7d 0a 80 01 00 00 00 00 2b 06 80 01 00 00 00 f0 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}.......+......................
9fa80 01 00 00 00 00 00 00 00 60 7b 0a 80 01 00 00 00 cc b0 05 80 01 00 00 00 07 00 00 00 00 00 00 00 ........`{......................
9faa0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 c0 77 0a 80 01 00 00 00 d0 1b 06 80 01 00 00 00 .................w..............
9fac0 17 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 28 79 0a 80 01 00 00 00 ........................(y......
9fae0 30 f5 05 80 01 00 00 00 c1 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 0...............................
9fb00 f0 7c 0a 80 01 00 00 00 00 ef 06 80 01 00 00 00 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .|..............................
9fb20 00 01 01 00 00 00 00 00 58 7a 0a 80 01 00 00 00 bc b2 05 80 01 00 00 00 07 00 00 00 00 00 00 00 ........Xz......................
9fb40 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 60 7d 0a 80 01 00 00 00 e0 47 06 80 01 00 00 00 ................`}.......G......
9fb60 e2 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 a8 7d 0a 80 01 00 00 00 .........................}......
9fb80 f0 cf 06 80 01 00 00 00 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9fba0 20 77 0a 80 01 00 00 00 f0 6e 06 80 01 00 00 00 c8 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .w.......n......................
9fbc0 01 00 00 00 00 00 00 00 e8 74 0a 80 01 00 00 00 08 16 06 80 01 00 00 00 23 00 00 00 00 00 00 00 .........t..............#.......
9fbe0 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 b8 75 0a 80 01 00 00 00 60 2a 06 80 01 00 00 00 .................u......`*......
9fc00 1a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 90 77 0a 80 01 00 00 00 .........................w......
9fc20 10 e8 05 80 01 00 00 00 1e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 ................................
9fc40 40 75 0a 80 01 00 00 00 c8 ee 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 @u..............................
9fc60 00 01 01 00 00 00 00 00 28 77 0a 80 01 00 00 00 c4 b0 05 80 01 00 00 00 06 00 00 00 00 00 00 00 ........(w......................
9fc80 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 70 7b 0a 80 01 00 00 00 c4 b0 05 80 01 00 00 00 ................p{..............
9fca0 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 78 7c 0a 80 01 00 00 00 ........................x|......
9fcc0 c0 7b 05 80 01 00 00 00 5d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 .{......].......................
9fce0 88 7e 0a 80 01 00 00 00 48 d0 06 80 01 00 00 00 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .~......H.......................
9fd00 00 01 01 00 00 00 00 00 18 81 0a 80 01 00 00 00 b8 8e 06 80 01 00 00 00 0f 00 00 00 00 00 00 00 ................................
9fd20 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 30 76 0a 80 01 00 00 00 00 b9 06 80 01 00 00 00 ................0v..............
9fd40 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 68 7d 0a 80 01 00 00 00 ........................h}......
9fd60 90 b2 05 80 01 00 00 00 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9fd80 78 7e 0a 80 01 00 00 00 b8 48 05 80 01 00 00 00 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 x~.......H......................
9fda0 00 01 01 00 00 00 00 00 58 7e 0a 80 01 00 00 00 c8 a5 06 80 01 00 00 00 0b 00 00 00 00 00 00 00 ........X~......................
9fdc0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 d8 7e 0a 80 01 00 00 00 a0 47 06 80 01 00 00 00 .................~.......G......
9fde0 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 b0 77 0a 80 01 00 00 00 .........................w......
9fe00 c0 9a 06 80 01 00 00 00 0f 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9fe20 a8 74 0a 80 01 00 00 00 b8 7b 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .t.......{......................
9fe40 01 00 01 00 00 00 00 00 c0 79 0a 80 01 00 00 00 14 7d 05 80 01 00 00 00 07 00 00 00 00 00 00 00 .........y.......}..............
9fe60 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 b8 76 0a 80 01 00 00 00 90 e6 06 80 01 00 00 00 .................v..............
9fe80 23 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 76 0a 80 01 00 00 00 #........................v......
9fea0 f4 c1 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
9fec0 60 76 0a 80 01 00 00 00 18 7b 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 `v.......{......................
9fee0 00 01 01 00 00 00 00 00 e8 7f 0a 80 01 00 00 00 60 a7 05 80 01 00 00 00 01 09 00 00 00 00 00 00 ................`...............
9ff00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 d8 7d 0a 80 01 00 00 00 6c b0 05 80 01 00 00 00 .................}......l.......
9ff20 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 98 78 0a 80 01 00 00 00 .........................x......
9ff40 10 47 06 80 01 00 00 00 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 .G..............................
9ff60 60 75 0a 80 01 00 00 00 e0 b2 05 80 01 00 00 00 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 `u..............................
9ff80 00 01 01 00 00 00 00 00 d0 7e 0a 80 01 00 00 00 b0 03 07 80 01 00 00 00 0e 00 00 00 00 00 00 00 .........~......................
9ffa0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 38 77 0a 80 01 00 00 00 30 5a 06 80 01 00 00 00 ................8w......0Z......
9ffc0 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 30 80 0a 80 01 00 00 00 ........................0.......
9ffe0 d8 b0 05 80 01 00 00 00 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
a0000 b0 74 0a 80 01 00 00 00 08 0d 07 80 01 00 00 00 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .t..............................
a0020 00 01 01 00 00 00 00 00 18 76 0a 80 01 00 00 00 e0 a5 06 80 01 00 00 00 09 00 00 00 00 00 00 00 .........v......................
a0040 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 48 80 0a 80 01 00 00 00 14 6c 05 80 01 00 00 00 ................H........l......
a0060 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 00 77 0a 80 01 00 00 00 .........................w......
a0080 14 6c 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 .l..............................
a00a0 c8 7c 0a 80 01 00 00 00 e8 ac 06 80 01 00 00 00 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .|..............................
a00c0 00 01 01 00 00 00 00 00 38 74 0a 80 01 00 00 00 f4 fd 05 80 01 00 00 00 05 00 00 00 00 00 00 00 ........8t......................
a00e0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 c8 7d 0a 80 01 00 00 00 a0 b1 05 80 01 00 00 00 .................}..............
a0100 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 48 77 0a 80 01 00 00 00 ........................Hw......
a0120 c4 99 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 ................................
a0140 98 7b 0a 80 01 00 00 00 c4 99 06 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .{..............................
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a01c0 40 b1 05 80 01 00 00 00 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 @...............................
a01e0 80 7d 0a 80 01 00 00 00 20 7d 05 80 01 00 00 00 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}.......}......................
a0200 00 01 01 00 00 00 00 00 e8 78 0a 80 01 00 00 00 ec b4 05 80 01 00 00 00 06 00 00 00 00 00 00 00 .........x......................
a0220 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 f0 7f 0a 80 01 00 00 00 ec b4 05 80 01 00 00 00 ................................
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a02c0 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 a8 75 0a 80 01 00 00 00 5c b1 05 80 01 00 00 00 .................u......\.......
a02e0 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 01 00 00 00 00 00 c0 7d 0a 80 01 00 00 00 .........................}......
a0300 5c b1 05 80 01 00 00 00 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 01 00 00 00 00 00 \...............................
a0320 a8 79 0a 80 01 00 00 00 c4 a6 06 80 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .y..............................
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a39e0 72 65 64 75 63 65 5f 63 79 74 68 6f 6e 5f 5f 00 56 69 65 77 2e 4d 65 6d 6f 72 79 56 69 65 77 2e reduce_cython__.View.MemoryView.
a3a00 61 72 72 61 79 2e 5f 5f 73 65 74 69 74 65 6d 5f 5f 00 00 00 00 00 00 00 56 69 65 77 2e 4d 65 6d array.__setitem__.......View.Mem
a3a20 6f 72 79 56 69 65 77 2e 61 72 72 61 79 2e 5f 5f 67 65 74 69 74 65 6d 5f 5f 00 00 00 00 00 00 00 oryView.array.__getitem__.......
a3a40 56 69 65 77 2e 4d 65 6d 6f 72 79 56 69 65 77 2e 61 72 72 61 79 2e 5f 5f 67 65 74 61 74 74 72 5f View.MemoryView.array.__getattr_
a3a60 5f 00 00 00 00 00 00 00 56 69 65 77 2e 4d 65 6d 6f 72 79 56 69 65 77 2e 61 72 72 61 79 2e 67 65 _.......View.MemoryView.array.ge
a3a80 74 5f 6d 65 6d 76 69 65 77 00 00 00 00 00 00 00 56 69 65 77 2e 4d 65 6d 6f 72 79 56 69 65 77 2e t_memview.......View.MemoryView.
a3aa0 61 72 72 61 79 2e 6d 65 6d 76 69 65 77 2e 5f 5f 67 65 74 5f 5f 00 00 00 56 69 65 77 2e 4d 65 6d array.memview.__get__...View.Mem
a3ac0 6f 72 79 56 69 65 77 2e 61 72 72 61 79 2e 5f 5f 67 65 74 62 75 66 66 65 72 5f 5f 00 00 00 00 00 oryView.array.__getbuffer__.....
a3ae0 50 79 4f 62 6a 65 63 74 5f 47 65 74 42 75 66 66 65 72 3a 20 76 69 65 77 3d 3d 4e 55 4c 4c 20 61 PyObject_GetBuffer:.view==NULL.a
a3b00 72 67 75 6d 65 6e 74 20 69 73 20 6f 62 73 6f 6c 65 74 65 00 00 00 00 00 56 69 65 77 2e 4d 65 6d rgument.is.obsolete.....View.Mem
a3b20 6f 72 79 56 69 65 77 2e 61 72 72 61 79 2e 5f 5f 63 69 6e 69 74 5f 5f 00 65 78 70 65 63 74 65 64 oryView.array.__cinit__.expected
a3b40 20 62 79 74 65 73 2c 20 4e 6f 6e 65 54 79 70 65 20 66 6f 75 6e 64 00 00 45 78 70 65 63 74 65 64 .bytes,.NoneType.found..Expected
a3b60 20 25 2e 31 36 73 2c 20 67 6f 74 20 25 2e 32 30 30 73 00 00 62 79 74 65 73 00 00 00 00 00 00 00 .%.16s,.got.%.200s..bytes.......
a3b80 6f 62 6a 65 63 74 20 6f 66 20 74 79 70 65 20 27 4e 6f 6e 65 54 79 70 65 27 20 68 61 73 20 6e 6f object.of.type.'NoneType'.has.no
a3ba0 20 6c 65 6e 28 29 00 00 41 72 67 75 6d 65 6e 74 20 27 25 2e 32 30 30 73 27 20 6d 75 73 74 20 6e .len()..Argument.'%.200s'.must.n
a3bc0 6f 74 20 62 65 20 4e 6f 6e 65 00 00 73 68 61 70 65 00 00 00 00 00 00 00 56 69 65 77 2e 4d 65 6d ot.be.None..shape.......View.Mem
a3be0 6f 72 79 56 69 65 77 2e 61 72 72 61 79 2e 5f 5f 63 69 6e 69 74 5f 5f 00 5f 5f 63 69 6e 69 74 5f oryView.array.__cinit__.__cinit_
a3c00 5f 00 00 00 00 00 00 00 5f 5f 63 69 6e 69 74 5f 5f 00 00 00 00 00 00 00 5f 5f 63 69 6e 69 74 5f _.......__cinit__.......__cinit_
a3c20 5f 00 00 00 00 00 00 00 5f 5f 63 69 6e 69 74 5f 5f 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 69 6d _.......__cinit__.......numpy.im
a3c40 70 6f 72 74 5f 61 72 72 61 79 00 00 00 00 00 00 6e 75 6d 70 79 2e 69 6d 70 6f 72 74 5f 61 72 72 port_array......numpy.import_arr
a3c60 61 79 00 00 00 00 00 00 6e 75 6d 70 79 2e 50 79 41 72 72 61 79 5f 4d 75 6c 74 69 49 74 65 72 4e ay......numpy.PyArray_MultiIterN
a3c80 65 77 33 00 00 00 00 00 6e 75 6d 70 79 2e 50 79 41 72 72 61 79 5f 4d 75 6c 74 69 49 74 65 72 4e ew3.....numpy.PyArray_MultiIterN
a3ca0 65 77 32 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e ew2.....numpy.random._generator.
a3cc0 64 65 66 61 75 6c 74 5f 72 6e 67 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 default_rng.....numpy.random._ge
a3ce0 6e 65 72 61 74 6f 72 2e 64 65 66 61 75 6c 74 5f 72 6e 67 00 00 00 00 00 64 65 66 61 75 6c 74 5f nerator.default_rng.....default_
a3d00 72 6e 67 00 00 00 00 00 64 65 66 61 75 6c 74 5f 72 6e 67 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 rng.....default_rng.....numpy.ra
a3d20 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 70 65 72 6d 75 74 ndom._generator.Generator.permut
a3d40 61 74 69 6f 6e 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e ation...numpy.random._generator.
a3d60 47 65 6e 65 72 61 74 6f 72 2e 70 65 72 6d 75 74 61 74 69 6f 6e 00 00 00 70 65 72 6d 75 74 61 74 Generator.permutation...permutat
a3d80 69 6f 6e 00 00 00 00 00 70 65 72 6d 75 74 61 74 69 6f 6e 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 ion.....permutation.....numpy.ra
a3da0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 73 68 75 66 66 6c ndom._generator.Generator.shuffl
a3dc0 65 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e e.......numpy.random._generator.
a3de0 47 65 6e 65 72 61 74 6f 72 2e 73 68 75 66 66 6c 65 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.shuffle.......numpy.ra
a3e00 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 73 68 75 66 66 6c ndom._generator.Generator.shuffl
a3e20 65 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e e.......numpy.random._generator.
a3e40 47 65 6e 65 72 61 74 6f 72 2e 73 68 75 66 66 6c 65 00 00 00 00 00 00 00 73 68 75 66 66 6c 65 00 Generator.shuffle.......shuffle.
a3e60 73 68 75 66 66 6c 65 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e shuffle.numpy.random._generator.
a3e80 47 65 6e 65 72 61 74 6f 72 2e 70 65 72 6d 75 74 65 64 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.permuted......numpy.ra
a3ea0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 70 65 72 6d 75 74 ndom._generator.Generator.permut
a3ec0 65 64 00 00 00 00 00 00 70 65 72 6d 75 74 65 64 00 00 00 00 00 00 00 00 70 65 72 6d 75 74 65 64 ed......permuted........permuted
a3ee0 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e ........numpy.random._generator.
a3f00 47 65 6e 65 72 61 74 6f 72 2e 64 69 72 69 63 68 6c 65 74 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.dirichlet.....numpy.ra
a3f20 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 64 69 72 69 63 68 ndom._generator.Generator.dirich
a3f40 6c 65 74 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e let.....numpy.random._generator.
a3f60 47 65 6e 65 72 61 74 6f 72 2e 64 69 72 69 63 68 6c 65 74 00 00 00 00 00 64 69 72 69 63 68 6c 65 Generator.dirichlet.....dirichle
a3f80 74 00 00 00 00 00 00 00 64 69 72 69 63 68 6c 65 74 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 t.......dirichlet.......numpy.ra
a3fa0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 76 ndom._generator.Generator.multiv
a3fc0 61 72 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 00 6e 75 6d 70 79 2e 72 61 ariate_hypergeometric...numpy.ra
a3fe0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 76 ndom._generator.Generator.multiv
a4000 61 72 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 00 6e 75 6d 70 79 2e 72 61 ariate_hypergeometric...numpy.ra
a4020 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 76 ndom._generator.Generator.multiv
a4040 61 72 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 00 6e 75 6d 70 79 2e 72 61 ariate_hypergeometric...numpy.ra
a4060 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 76 ndom._generator.Generator.multiv
a4080 61 72 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 00 6d 75 6c 74 69 76 61 72 ariate_hypergeometric...multivar
a40a0 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 00 00 00 6d 75 6c 74 69 76 61 72 iate_hypergeometric.....multivar
a40c0 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 00 00 00 6d 75 6c 74 69 76 61 72 iate_hypergeometric.....multivar
a40e0 69 61 74 65 5f 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 iate_hypergeometric.....numpy.ra
a4100 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 6e ndom._generator.Generator.multin
a4120 6f 6d 69 61 6c 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e omial...numpy.random._generator.
a4140 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 6e 6f 6d 69 61 6c 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.multinomial...numpy.ra
a4160 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 6e ndom._generator.Generator.multin
a4180 6f 6d 69 61 6c 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e omial...numpy.random._generator.
a41a0 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 6e 6f 6d 69 61 6c 00 00 00 6d 75 6c 74 69 6e 6f 6d Generator.multinomial...multinom
a41c0 69 61 6c 00 00 00 00 00 6d 75 6c 74 69 6e 6f 6d 69 61 6c 00 00 00 00 00 6d 75 6c 74 69 6e 6f 6d ial.....multinomial.....multinom
a41e0 69 61 6c 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e ial.....numpy.random._generator.
a4200 47 65 6e 65 72 61 74 6f 72 2e 6d 75 6c 74 69 76 61 72 69 61 74 65 5f 6e 6f 72 6d 61 6c 00 00 00 Generator.multivariate_normal...
a4220 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4240 72 2e 6d 75 6c 74 69 76 61 72 69 61 74 65 5f 6e 6f 72 6d 61 6c 00 00 00 6d 75 6c 74 69 76 61 72 r.multivariate_normal...multivar
a4260 69 61 74 65 5f 6e 6f 72 6d 61 6c 00 00 00 00 00 6d 75 6c 74 69 76 61 72 69 61 74 65 5f 6e 6f 72 iate_normal.....multivariate_nor
a4280 6d 61 6c 00 00 00 00 00 6d 75 6c 74 69 76 61 72 69 61 74 65 5f 6e 6f 72 6d 61 6c 00 00 00 00 00 mal.....multivariate_normal.....
a42a0 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a42c0 72 2e 6c 6f 67 73 65 72 69 65 73 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.logseries.....numpy.random._ge
a42e0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6c 6f 67 73 65 72 69 65 73 00 00 00 00 00 nerator.Generator.logseries.....
a4300 6c 6f 67 73 65 72 69 65 73 00 00 00 00 00 00 00 6c 6f 67 73 65 72 69 65 73 00 00 00 00 00 00 00 logseries.......logseries.......
a4320 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4340 72 2e 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 r.hypergeometric........numpy.ra
a4360 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 68 79 70 65 72 67 ndom._generator.Generator.hyperg
a4380 65 6f 6d 65 74 72 69 63 00 00 00 00 00 00 00 00 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 eometric........hypergeometric..
a43a0 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 hypergeometric..hypergeometric..
a43c0 68 79 70 65 72 67 65 6f 6d 65 74 72 69 63 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 hypergeometric..numpy.random._ge
a43e0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 67 65 6f 6d 65 74 72 69 63 00 00 00 00 00 nerator.Generator.geometric.....
a4400 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4420 72 2e 67 65 6f 6d 65 74 72 69 63 00 00 00 00 00 67 65 6f 6d 65 74 72 69 63 00 00 00 00 00 00 00 r.geometric.....geometric.......
a4440 67 65 6f 6d 65 74 72 69 63 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 geometric.......numpy.random._ge
a4460 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 7a 69 70 66 00 00 6e 75 6d 70 79 2e 72 61 nerator.Generator.zipf..numpy.ra
a4480 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 7a 69 70 66 00 00 ndom._generator.Generator.zipf..
a44a0 7a 69 70 66 00 00 00 00 7a 69 70 66 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 zipf....zipf....numpy.random._ge
a44c0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 70 6f 69 73 73 6f 6e 00 00 00 00 00 00 00 nerator.Generator.poisson.......
a44e0 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4500 72 2e 70 6f 69 73 73 6f 6e 00 00 00 00 00 00 00 70 6f 69 73 73 6f 6e 00 70 6f 69 73 73 6f 6e 00 r.poisson.......poisson.poisson.
a4520 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4540 72 2e 6e 65 67 61 74 69 76 65 5f 62 69 6e 6f 6d 69 61 6c 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 r.negative_binomial.....numpy.ra
a4560 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6e 65 67 61 74 69 ndom._generator.Generator.negati
a4580 76 65 5f 62 69 6e 6f 6d 69 61 6c 00 00 00 00 00 6e 65 67 61 74 69 76 65 5f 62 69 6e 6f 6d 69 61 ve_binomial.....negative_binomia
a45a0 6c 00 00 00 00 00 00 00 6e 65 67 61 74 69 76 65 5f 62 69 6e 6f 6d 69 61 6c 00 00 00 00 00 00 00 l.......negative_binomial.......
a45c0 6e 65 67 61 74 69 76 65 5f 62 69 6e 6f 6d 69 61 6c 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 negative_binomial.......numpy.ra
a45e0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 62 69 6e 6f 6d 69 ndom._generator.Generator.binomi
a4600 61 6c 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e al......numpy.random._generator.
a4620 47 65 6e 65 72 61 74 6f 72 2e 62 69 6e 6f 6d 69 61 6c 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.binomial......numpy.ra
a4640 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 62 69 6e 6f 6d 69 ndom._generator.Generator.binomi
a4660 61 6c 00 00 00 00 00 00 62 69 6e 6f 6d 69 61 6c 00 00 00 00 00 00 00 00 62 69 6e 6f 6d 69 61 6c al......binomial........binomial
a4680 00 00 00 00 00 00 00 00 62 69 6e 6f 6d 69 61 6c 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 ........binomial........numpy.ra
a46a0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 74 72 69 61 6e 67 ndom._generator.Generator.triang
a46c0 75 6c 61 72 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e ular....numpy.random._generator.
a46e0 47 65 6e 65 72 61 74 6f 72 2e 74 72 69 61 6e 67 75 6c 61 72 00 00 00 00 74 72 69 61 6e 67 75 6c Generator.triangular....triangul
a4700 61 72 00 00 00 00 00 00 74 72 69 61 6e 67 75 6c 61 72 00 00 00 00 00 00 74 72 69 61 6e 67 75 6c ar......triangular......triangul
a4720 61 72 00 00 00 00 00 00 74 72 69 61 6e 67 75 6c 61 72 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 ar......triangular......numpy.ra
a4740 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 77 61 6c 64 00 00 ndom._generator.Generator.wald..
a4760 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4780 72 2e 77 61 6c 64 00 00 77 61 6c 64 00 00 00 00 77 61 6c 64 00 00 00 00 77 61 6c 64 00 00 00 00 r.wald..wald....wald....wald....
a47a0 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a47c0 72 2e 72 61 79 6c 65 69 67 68 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.rayleigh......numpy.random._ge
a47e0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 72 61 79 6c 65 69 67 68 00 00 00 00 00 00 nerator.Generator.rayleigh......
a4800 72 61 79 6c 65 69 67 68 00 00 00 00 00 00 00 00 72 61 79 6c 65 69 67 68 00 00 00 00 00 00 00 00 rayleigh........rayleigh........
a4820 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4840 72 2e 6c 6f 67 6e 6f 72 6d 61 6c 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.lognormal.....numpy.random._ge
a4860 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6c 6f 67 6e 6f 72 6d 61 6c 00 00 00 00 00 nerator.Generator.lognormal.....
a4880 6c 6f 67 6e 6f 72 6d 61 6c 00 00 00 00 00 00 00 6c 6f 67 6e 6f 72 6d 61 6c 00 00 00 00 00 00 00 lognormal.......lognormal.......
a48a0 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a48c0 72 2e 6c 6f 67 69 73 74 69 63 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.logistic......numpy.random._ge
a48e0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6c 6f 67 69 73 74 69 63 00 00 00 00 00 00 nerator.Generator.logistic......
a4900 6c 6f 67 69 73 74 69 63 00 00 00 00 00 00 00 00 6c 6f 67 69 73 74 69 63 00 00 00 00 00 00 00 00 logistic........logistic........
a4920 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4940 72 2e 67 75 6d 62 65 6c 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.gumbel........numpy.random._ge
a4960 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 67 75 6d 62 65 6c 00 00 00 00 00 00 00 00 nerator.Generator.gumbel........
a4980 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a49a0 72 2e 6c 61 70 6c 61 63 65 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.laplace.......numpy.random._ge
a49c0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6c 61 70 6c 61 63 65 00 00 00 00 00 00 00 nerator.Generator.laplace.......
a49e0 6c 61 70 6c 61 63 65 00 6c 61 70 6c 61 63 65 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 laplace.laplace.numpy.random._ge
a4a00 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 70 6f 77 65 72 00 6e 75 6d 70 79 2e 72 61 nerator.Generator.power.numpy.ra
a4a20 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 70 6f 77 65 72 00 ndom._generator.Generator.power.
a4a40 70 6f 77 65 72 00 00 00 70 6f 77 65 72 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 power...power...numpy.random._ge
a4a60 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 77 65 69 62 75 6c 6c 00 00 00 00 00 00 00 nerator.Generator.weibull.......
a4a80 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4aa0 72 2e 77 65 69 62 75 6c 6c 00 00 00 00 00 00 00 77 65 69 62 75 6c 6c 00 77 65 69 62 75 6c 6c 00 r.weibull.......weibull.weibull.
a4ac0 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4ae0 72 2e 70 61 72 65 74 6f 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.pareto........numpy.random._ge
a4b00 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 70 61 72 65 74 6f 00 00 00 00 70 61 72 65 nerator.Generator.pareto....pare
a4b20 74 6f 00 00 70 61 72 65 74 6f 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 to..pareto......numpy.random._ge
a4b40 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 76 6f 6e 6d 69 73 65 73 00 00 00 00 00 00 nerator.Generator.vonmises......
a4b60 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4b80 72 2e 76 6f 6e 6d 69 73 65 73 00 00 00 00 00 00 76 6f 6e 6d 69 73 65 73 00 00 00 00 00 00 00 00 r.vonmises......vonmises........
a4ba0 76 6f 6e 6d 69 73 65 73 00 00 00 00 00 00 00 00 76 6f 6e 6d 69 73 65 73 00 00 00 00 00 00 00 00 vonmises........vonmises........
a4bc0 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4be0 72 2e 73 74 61 6e 64 61 72 64 5f 74 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.standard_t....numpy.random._ge
a4c00 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 72 64 5f 74 00 00 00 00 nerator.Generator.standard_t....
a4c20 73 74 61 6e 64 61 72 64 5f 74 00 00 00 00 00 00 73 74 61 6e 64 61 72 64 5f 74 00 00 00 00 00 00 standard_t......standard_t......
a4c40 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4c60 72 2e 73 74 61 6e 64 61 72 64 5f 63 61 75 63 68 79 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 r.standard_cauchy.......numpy.ra
a4c80 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 ndom._generator.Generator.standa
a4ca0 72 64 5f 63 61 75 63 68 79 00 00 00 00 00 00 00 73 74 61 6e 64 61 72 64 5f 63 61 75 63 68 79 00 rd_cauchy.......standard_cauchy.
a4cc0 73 74 61 6e 64 61 72 64 5f 63 61 75 63 68 79 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 standard_cauchy.numpy.random._ge
a4ce0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6e 6f 6e 63 65 6e 74 72 61 6c 5f 63 68 69 nerator.Generator.noncentral_chi
a4d00 73 71 75 61 72 65 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e square..numpy.random._generator.
a4d20 47 65 6e 65 72 61 74 6f 72 2e 6e 6f 6e 63 65 6e 74 72 61 6c 5f 63 68 69 73 71 75 61 72 65 00 00 Generator.noncentral_chisquare..
a4d40 6e 6f 6e 63 65 6e 74 72 61 6c 5f 63 68 69 73 71 75 61 72 65 00 00 00 00 6e 6f 6e 63 65 6e 74 72 noncentral_chisquare....noncentr
a4d60 61 6c 5f 63 68 69 73 71 75 61 72 65 00 00 00 00 6e 6f 6e 63 65 6e 74 72 61 6c 5f 63 68 69 73 71 al_chisquare....noncentral_chisq
a4d80 75 61 72 65 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e uare....numpy.random._generator.
a4da0 47 65 6e 65 72 61 74 6f 72 2e 63 68 69 73 71 75 61 72 65 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.chisquare.....numpy.ra
a4dc0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 63 68 69 73 71 75 ndom._generator.Generator.chisqu
a4de0 61 72 65 00 00 00 00 00 63 68 69 73 71 75 61 72 65 00 00 00 00 00 00 00 63 68 69 73 71 75 61 72 are.....chisquare.......chisquar
a4e00 65 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e e.......numpy.random._generator.
a4e20 47 65 6e 65 72 61 74 6f 72 2e 6e 6f 6e 63 65 6e 74 72 61 6c 5f 66 00 00 6e 75 6d 70 79 2e 72 61 Generator.noncentral_f..numpy.ra
a4e40 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6e 6f 6e 63 65 6e ndom._generator.Generator.noncen
a4e60 74 72 61 6c 5f 66 00 00 6e 6f 6e 63 65 6e 74 72 61 6c 5f 66 00 00 00 00 6e 6f 6e 63 65 6e 74 72 tral_f..noncentral_f....noncentr
a4e80 61 6c 5f 66 00 00 00 00 6e 6f 6e 63 65 6e 74 72 61 6c 5f 66 00 00 00 00 6e 6f 6e 63 65 6e 74 72 al_f....noncentral_f....noncentr
a4ea0 61 6c 5f 66 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e al_f....numpy.random._generator.
a4ec0 47 65 6e 65 72 61 74 6f 72 2e 66 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 Generator.f.....numpy.random._ge
a4ee0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 66 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 nerator.Generator.f.....numpy.ra
a4f00 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 67 61 6d 6d 61 00 ndom._generator.Generator.gamma.
a4f20 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a4f40 72 2e 67 61 6d 6d 61 00 67 61 6d 6d 61 00 00 00 67 61 6d 6d 61 00 00 00 6e 75 6d 70 79 2e 72 61 r.gamma.gamma...gamma...numpy.ra
a4f60 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 ndom._generator.Generator.standa
a4f80 72 64 5f 67 61 6d 6d 61 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 rd_gamma........numpy.random._ge
a4fa0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 72 64 5f 67 61 6d 6d 61 nerator.Generator.standard_gamma
a4fc0 00 00 00 00 00 00 00 00 73 74 61 6e 64 61 72 64 5f 67 61 6d 6d 61 00 00 73 74 61 6e 64 61 72 64 ........standard_gamma..standard
a4fe0 5f 67 61 6d 6d 61 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e _gamma..numpy.random._generator.
a5000 47 65 6e 65 72 61 74 6f 72 2e 6e 6f 72 6d 61 6c 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.normal........numpy.ra
a5020 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 6e 6f 72 6d 61 6c ndom._generator.Generator.normal
a5040 00 00 00 00 6e 6f 72 6d 61 6c 00 00 6e 6f 72 6d 61 6c 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 ....normal..normal......numpy.ra
a5060 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 ndom._generator.Generator.standa
a5080 72 64 5f 6e 6f 72 6d 61 6c 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 rd_normal.......numpy.random._ge
a50a0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 72 64 5f 6e 6f 72 6d 61 nerator.Generator.standard_norma
a50c0 6c 00 00 00 00 00 00 00 73 74 61 6e 64 61 72 64 5f 6e 6f 72 6d 61 6c 00 73 74 61 6e 64 61 72 64 l.......standard_normal.standard
a50e0 5f 6e 6f 72 6d 61 6c 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e _normal.numpy.random._generator.
a5100 47 65 6e 65 72 61 74 6f 72 2e 75 6e 69 66 6f 72 6d 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.uniform.......numpy.ra
a5120 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 75 6e 69 66 6f 72 ndom._generator.Generator.unifor
a5140 6d 00 00 00 00 00 00 00 75 6e 69 66 6f 72 6d 00 75 6e 69 66 6f 72 6d 00 6e 75 6d 70 79 2e 72 61 m.......uniform.uniform.numpy.ra
a5160 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 63 68 6f 69 63 65 ndom._generator.Generator.choice
a5180 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e ........numpy.random._generator.
a51a0 47 65 6e 65 72 61 74 6f 72 2e 63 68 6f 69 63 65 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.choice........numpy.ra
a51c0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 63 68 6f 69 63 65 ndom._generator.Generator.choice
a51e0 00 00 00 00 63 68 6f 69 63 65 00 00 63 68 6f 69 63 65 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 ....choice..choice......numpy.ra
a5200 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 62 79 74 65 73 00 ndom._generator.Generator.bytes.
a5220 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a5240 72 2e 62 79 74 65 73 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e r.bytes.numpy.random._generator.
a5260 47 65 6e 65 72 61 74 6f 72 2e 69 6e 74 65 67 65 72 73 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.integers......numpy.ra
a5280 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 69 6e 74 65 67 65 ndom._generator.Generator.intege
a52a0 72 73 00 00 00 00 00 00 69 6e 74 65 67 65 72 73 00 00 00 00 00 00 00 00 69 6e 74 65 67 65 72 73 rs......integers........integers
a52c0 00 00 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e ........numpy.random._generator.
a52e0 47 65 6e 65 72 61 74 6f 72 2e 73 74 61 6e 64 61 72 64 5f 65 78 70 6f 6e 65 6e 74 69 61 6c 00 00 Generator.standard_exponential..
a5300 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a5320 72 2e 73 74 61 6e 64 61 72 64 5f 65 78 70 6f 6e 65 6e 74 69 61 6c 00 00 73 74 61 6e 64 61 72 64 r.standard_exponential..standard
a5340 5f 65 78 70 6f 6e 65 6e 74 69 61 6c 00 00 00 00 73 74 61 6e 64 61 72 64 5f 65 78 70 6f 6e 65 6e _exponential....standard_exponen
a5360 74 69 61 6c 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e tial....numpy.random._generator.
a5380 47 65 6e 65 72 61 74 6f 72 2e 65 78 70 6f 6e 65 6e 74 69 61 6c 00 00 00 6e 75 6d 70 79 2e 72 61 Generator.exponential...numpy.ra
a53a0 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 65 78 70 6f 6e 65 ndom._generator.Generator.expone
a53c0 6e 74 69 61 6c 00 00 00 65 78 70 6f 6e 65 6e 74 69 61 6c 00 00 00 00 00 65 78 70 6f 6e 65 6e 74 ntial...exponential.....exponent
a53e0 69 61 6c 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e ial.....numpy.random._generator.
a5400 47 65 6e 65 72 61 74 6f 72 2e 62 65 74 61 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 Generator.beta..numpy.random._ge
a5420 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 62 65 74 61 00 00 62 65 74 61 00 00 00 00 nerator.Generator.beta..beta....
a5440 62 65 74 61 00 00 00 00 62 65 74 61 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 beta....beta....numpy.random._ge
a5460 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 72 61 6e 64 6f 6d 00 00 00 00 00 00 00 00 nerator.Generator.random........
a5480 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a54a0 72 2e 72 61 6e 64 6f 6d 00 00 00 00 72 61 6e 64 6f 6d 00 00 72 61 6e 64 6f 6d 00 00 00 00 00 00 r.random....random..random......
a54c0 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a54e0 72 2e 5f 5f 72 65 64 75 63 65 5f 5f 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.__reduce__....numpy.random._ge
a5500 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 5f 5f 73 65 74 73 74 61 74 65 5f 5f 00 00 nerator.Generator.__setstate__..
a5520 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a5540 72 2e 5f 5f 67 65 74 73 74 61 74 65 5f 5f 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.__getstate__..numpy.random._ge
a5560 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 5f 5f 73 74 72 5f 5f 00 00 00 00 00 00 00 nerator.Generator.__str__.......
a5580 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f numpy.random._generator.Generato
a55a0 72 2e 5f 5f 72 65 70 72 5f 5f 00 00 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 r.__repr__......numpy.random._ge
a55c0 6e 65 72 61 74 6f 72 2e 47 65 6e 65 72 61 74 6f 72 2e 5f 5f 69 6e 69 74 5f 5f 00 00 00 00 00 00 nerator.Generator.__init__......
a55e0 42 69 74 47 65 6e 65 72 61 74 6f 72 00 00 00 00 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 BitGenerator....numpy.random._ge
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a5640 6e 75 6d 70 79 2e 72 61 6e 64 6f 6d 2e 5f 67 65 6e 65 72 61 74 6f 72 2e 5f 63 68 65 63 6b 5f 62 numpy.random._generator._check_b
a5660 69 74 5f 67 65 6e 65 72 61 74 6f 72 00 00 00 00 42 69 74 47 65 6e 65 72 61 74 6f 72 00 00 00 00 it_generator....BitGenerator....
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