Simulating from a multinomial distribution with large number of categories

The multinomial distribution is a key-distribution for several applications. For this reason, many methods have been proposed so far in the literature in order to deal with the problem of simulation from it. A slight modification is suggested which can be used in conjunction with any of the standard schemes. The proposed variation is a two-stage procedure based on the property of the multinomial distribution that for any partition of the set of outcomes the vector of total frequencies of each part follows also a multinomial distribution with parameters adjusted accordingly. It is empirically exhibited that this variation is faster than the original procedures in case the numbers of independent trials and possible outcomes are both large. The time reduction is illustrated via a simulation study for several programming languages such as R, Matlab, and others.