A simple algorithm for generating multinomial random vectors with extravariation

An algorithm for generating vectors of counts with extravariation is presented. The algorithm produces a random vector whose distribution is a finite mixture of multinomial random vectors. The proposed distribution matches the first two moments of the Dirichlet-multinomial distribution and coincides with the latter when clusters contain two elements. In a Monte Carlo study, goodness-of-fit tests for data generated under both the Dirichlet-multinomial and the finite mixture distributions are examined.