Sampling from binomial and Poisson distributions: a method with bounded computation times

n accurate acceptance-rejection algorithm is devised and tested. The procedure requires an average of less than 3 uniform deviates whenever the standard deviation σ of the distribution is at least 4, and this number decreases monotonically to 2.63 as σ→∞. Variable parameters are permitted, and no subroutines for sampling from other statistical distributions are needed.