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Convexity Properties of Some Entropies

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Abstract

We consider a family of probability distributions depending on a real parameter x, and study the logarithmic convexity of the sum of the squared probabilities. Applications concerning bounds and concavity properties of Rényi and Tsallis entropies are given. Finally, some extensions and an open problem are presented.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Cluj-Napoca, Memorandumului Street 28, 400114, Cluj-Napoca, Romania

    Ioan Raşa

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  1. Ioan Raşa
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Correspondence to Ioan Raşa.

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Dedicated to Professor Heiner Gonska on the occasion of his 70th birthday.

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Raşa, I. Convexity Properties of Some Entropies. Results Math 73, 105 (2018). https://doi.org/10.1007/s00025-018-0868-8

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  • DOI: https://doi.org/10.1007/s00025-018-0868-8

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