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[37] | 1 | function r = randbinom(p, n) |
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| 2 | %RANDBINOM Sample from a binomial distribution. |
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| 3 | % RANDBINOM(P,N) returns a sample from a binomial distribution with |
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| 4 | % parameters P and N (scalars). Each sample ranges 0 to N. |
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| 5 | % It is more efficient than BINORND in the statistics toolbox. |
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| 6 | |
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| 7 | % References: |
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| 8 | % [1] L. Devroye, "Non-Uniform Random Variate Generation", |
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| 9 | % Springer-Verlag, 1986 |
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| 10 | % |
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| 11 | % Also see: Kachitvichyanukul, V., and Schmeiser, B. W. |
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| 12 | % "Binomial Random Variate Generation." Comm. ACM, 31, 2 (Feb. 1988), 216. |
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| 13 | |
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| 14 | % Written by Tom Minka |
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| 15 | |
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| 16 | if isnan(p) | isnan(n) |
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| 17 | r = nan; |
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| 18 | return |
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| 19 | end |
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| 20 | |
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| 21 | if n < 15 |
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| 22 | |
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| 23 | % coin flip method |
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| 24 | % this takes O(n) time |
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| 25 | r = 0; |
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| 26 | for i = 1:n |
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| 27 | if rand < p |
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| 28 | r = r + 1; |
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| 29 | end |
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| 30 | end |
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| 31 | |
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| 32 | elseif n*p < 150 |
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| 33 | |
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| 34 | % waiting time method |
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| 35 | % this takes O(np) time |
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| 36 | q = -log(1-p); |
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| 37 | r = n; |
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| 38 | e = -log(rand); |
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| 39 | s = e/r; |
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| 40 | while(s <= q) |
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| 41 | r = r - 1; |
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| 42 | if r == 0 |
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| 43 | break |
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| 44 | end |
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| 45 | e = -log(rand); |
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| 46 | s = s + e/r; |
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| 47 | end |
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| 48 | r = n - r; |
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| 49 | |
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| 50 | else |
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| 51 | |
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| 52 | % recursive method |
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| 53 | % this makes O(log(log(n))) recursive calls |
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| 54 | i = floor(p*(n+1)); |
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| 55 | b = randbeta(i, n+1-i); |
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| 56 | if b <= p |
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| 57 | r = i + randbinom((p-b)/(1-b), n-i); |
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| 58 | else |
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| 59 | r = i - 1 - randbinom((b-p)/b, i-1); |
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| 60 | end |
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| 61 | |
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| 62 | end |
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