Algorithm to generate Poisson and binomial random numbers?

Poisson distribution

Here’s how Wikipedia says Knuth says to do it:

init:
     Let L ← e^(−λ), k ← 0 and p ← 1.
do:
     k ← k + 1.
     Generate uniform random number u in [0,1] and let p ← p × u.
while p > L.
return k − 1.

In Java, that would be:

public static int getPoisson(double lambda) {
  double L = Math.exp(-lambda);
  double p = 1.0;
  int k = 0;

  do {
    k++;
    p *= Math.random();
  } while (p > L);

  return k - 1;
}

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Binomial distribution

Going by chapter 10 of Non-Uniform Random Variate Generation (PDF) by Luc Devroye (which I found linked from the Wikipedia article) gives this:

public static int getBinomial(int n, double p) {
  int x = 0;
  for(int i = 0; i < n; i++) {
    if(Math.random() < p)
      x++;
  }
  return x;
}

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Please note

Neither of these algorithms is optimal. The first is O(λ), the second is O(n). Depending on how large these values typically are, and how frequently you need to call the generators, you might need a better algorithm. The paper I link to above has more complicated algorithms that run in constant time, but I’ll leave those implementations as an exercise for the reader. 🙂