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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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