Expressions for the Entropy of Binomial-Type Distributions

TL;DR

This paper introduces a general method for calculating the entropy of various binomial-type distributions, providing series expansions, integral representations, and connections to special functions like the Riemann zeta function.

Contribution

It presents a novel unified approach to derive entropy formulas for multiple distributions, linking entropy to advanced mathematical functions.

Findings

Derived series expansions for distribution entropies

Established integral representations of entropy functions

Connected entropy calculations to the Riemann zeta function

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.