Expressions for the Entropy of Binomial-Type Distributions
Information Theory
2018-07-24 v4 math.IT
Probability
Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1708.06394,
title = {Expressions for the Entropy of Binomial-Type Distributions},
author = {Mahdi Cheraghchi},
journal= {arXiv preprint arXiv:1708.06394},
year = {2018}
}
Comments
A preliminary version of this work appears in Proceedings of the 2018 IEEE International Symposium on Information Theory (ISIT)