Complete monotonicity of some entropies

TL;DR

This paper investigates the complete monotonicity properties of Shannon, Rényi, and Tsallis entropies for a family of parameterized distributions including binomial, Poisson, and negative binomial, revealing new mathematical insights.

Contribution

It introduces the analysis of complete monotonicity of various entropies for common discrete distributions, extending understanding beyond traditional concavity properties.

Findings

Shannon, Rényi, and Tsallis entropies exhibit complete monotonicity for the considered distributions.

The results provide new mathematical characterizations of entropy functions.

Implications for information theory and statistical modeling are discussed.

Abstract

It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and negative binomial distributions) and investigate the Shannon, R\'{e}nyi, and Tsallis entropies of them with respect to the complete monotonicity.