Computer methods for sampling from gamma, beta, Poisson and binomial distributions

Accurate computer methods are evaluated which transform uniformly distributed random numbers into quantities that follow gamma, beta, Poisson, binomial and negative-binomial distributions. All algorithms are designed for variable parameters. The known convenient methods are slow when the parameters are large. Therefore new procedures are introduced which can cope efficiently with parameters of all sizes. Some algorithms require sampling from the normal distribution as an intermediate step. In the reported computer experiments the normal deviates were obtained from a recent method which is also described.