The computer generation of multinomial random variates

Abstract

The generation of random variates from the multinomial distribution is often required in simulation studies involving methods for the analysis of discrete data. Although several methods have been proposed, comprehensive comparisons of the various algorithms have not been previously carried out. This paper describes seven methods for multinomial variate generation and compares them with respect to the criteria of accuracy, set-up time, simplicity of implementation, storage requirements, and generation time. Based on the results of an extensive empirical study, the Brown and Bromberg ( Amer. Statist. 38, 1984) two-stage procedure is generally the fastest algorithm, but requires a complicated set-up phase and extensive storage requirements. The conditional distribution method using the modal binomial variate generator of Kemp ( Commun. Statist.—Theor. Meth. 15, 1986) is shown to be a good all-purpose algorithm, in that it has wide applicability, does not require a set-up phase and extensive storage, and is reasonably competitive with the Brown—Bromberg algorithm in terms of generation time.