Rapid Generation of Frequency Tables

This paper is concerned with situations where random samples of size n, from a discrete distribution, are required in the form of frequency tables rather than as streams of n individual variables. Instead of constructing each table by generating n observations and collecting them together, each table is generated directly by regarding it as a single sample from a multinomial distribution whose index is n and whose probabilities are those of the target distribution placed in decreasing order of magnitude. Sampling is achieved by a series of conditional binomial generations using a fast ‘variable‐parameter’ algorithm due to Kemp (1986). Results are presented which show that the new direct procedure is generally far faster than the standard indirect procedure using the very fast alias method to generate individual observations. Extensions to bivariate discrete distributions and to continuous distributions are noted.