Asymptotics of Entropy of the Dirichlet-Multinomial Distribution

Dirichlet distribution and multinomial distribution play important role in information theory and statistics. They find applications in estimation, average minimax redundancy in source coding, Pólya urn model, and graph compression. Dirichlet-multinomial distribution is a multinomial distribution in which parameters are distributed according to the Dirichlet distribution. In this paper, we present some characteristics of the Dirichlet-multinomial distribution, including a precise asymptotic for the entropy. It should be point out that such a characterization turns out to be technically quite challenging requiring analytic tools including analytic continuation of hypergeometric series.