Inequalities related to some types of entropies and divergences

Shigeru Furuichi and Nicuşor Minculete

Physica A: Statistical Mechanics and its Applications, 2019, vol. 532, issue C

Abstract: The aim of this paper is to discuss new results concerning some kinds of parametric extended entropies and divergences. As a result of our studies for mathematical properties on entropy and divergence, we give new bounds for the Tsallis quasilinear entropy and divergence by applying the Hermite-Hadamard inequality. We also give bounds for biparametric extended entropies and divergences which have been given in Furuichi (2010). In addition, we study (r,q)-quasilinear entropies and divergences as alternative biparametric extended entropy and divergence, and then we give bounds for them. Finally we obtain inequalities for an extended Lin’s divergence and some characterizations of Fermi-Dirac entropy and Bose-Einstein entropy.

Keywords: Shannon entropy; Divergence (relative entropy); Tsallis entropy; Rényi entropy; Biparametric extended entropy and biparametric extended divergence (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119311227

DOI: 10.1016/j.physa.2019.121907

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