Expressions for the Entropy of Binomial-Type Distributions

Abstract

We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, negative binomial, and hypergeometric distributions. Our results also establish connections between the entropy functions and to the Riemann zeta function and its generalizations.

arXiv commentA preliminary version of this work appears in Proceedings of the 2018 IEEE International Symposium on Information Theory (ISIT)