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Periodica Mathematica Hungarica

, Volume 75, Issue 2, pp 159–166 | Cite as

Complete monotonicity of some entropies

  • Ioan RaşaEmail author
Article
  • 103 Downloads

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 their Shannon, Rényi, and Tsallis entropies with respect to complete monotonicity.

Keywords

Entropies Concavity Complete monotonicity Inequalities 

Mathematics Subject Classification

94A17 60E15 26A51 

Notes

Acknowledgements

The author is grateful to the referee for valuable comments and very constructive suggestions. In particular, the elegant alternative proofs presented in Remark 2.4 were kindly suggested by the referee.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

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