Sampling from the Binomial Distribution on a Computer

This article describes a method of sampling from the binomial distribution (B(n, p) that appears less costly than the beta method recently suggested by Relies (1972) and Ahrens and Dieter (1974). The method uses the acceptance-rejection technique together with an efficient sampling algorithm for the Poisson distribution (Fishman 1976) to provide a binomial variate with cost proportional to {n min[p/(1 — p), (1 — p)/p]}1/2. The article also assesses the use of a normal approximation for the Poisson distribution for n min(p, 1 — p) ≥ 15 and shows the additional saving as a function of n and p.