TL;DR
This paper investigates the concavity properties of Shannon, Rényi, and Tsallis entropies for a family of distributions including binomial, Poisson, and negative binomial, extending known results about entropy functions.
Contribution
It provides a comprehensive analysis of the concavity of various entropies for these distributions, which was previously not fully understood.
Findings
Shannon entropy is concave for the considered distributions.
Rényi and Tsallis entropies exhibit concavity under certain conditions.
The results extend the understanding of entropy behavior in parameterized distributions.
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 concavity of the Shannon, R\'enyi, and Tsallis entropies of them.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Fractional Differential Equations Solutions · Statistical Distribution Estimation and Applications