Convexity and robustness of the Rényi entropy

We study convexity properties of the Rényi entropy as function of $\alpha >0$ on finite alphabets. We also describe robustness of the Rényi entropy on finite alphabets, and it turns out that the rate of respective convergence depends on initial alphabet. We establish convergence of the disturbed...

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Main Authors:	Filipp Buryak, Yuliya Mishura
Format:	Article
Language:	English
Published:	VTeX 2021-07-01
Series:	Modern Stochastics: Theory and Applications
Subjects:	Discrete distribution Rényi entropy convexity
Online Access:	https://www.vmsta.org/doi/10.15559/21-VMSTA185

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spelling	doaj-eee92ef245cc4b359c0050e76dd5c58d2021-09-15T11:50:20ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542021-07-018338741210.15559/21-VMSTA185Convexity and robustness of the Rényi entropyFilipp Buryak0Yuliya Mishura1Kyiv National Taras Shevchenko University, Faculty of Mechanics and Mathematics, Department of Probability Theory, Statistics and Actuarial Mathematics, Volodymyrska 64, 01601 Kyiv, UkraineKyiv National Taras Shevchenko University, Faculty of Mechanics and Mathematics, Department of Probability Theory, Statistics and Actuarial Mathematics, Volodymyrska 64, 01601 Kyiv, UkraineWe study convexity properties of the Rényi entropy as function of $\alpha >0$ on finite alphabets. We also describe robustness of the Rényi entropy on finite alphabets, and it turns out that the rate of respective convergence depends on initial alphabet. We establish convergence of the disturbed entropy when the initial distribution is uniform but the number of events increases to ∞ and prove that the limit of Rényi entropy of the binomial distribution is equal to Rényi entropy of the Poisson distribution.https://www.vmsta.org/doi/10.15559/21-VMSTA185Discrete distributionRényi entropyconvexity
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Filipp Buryak Yuliya Mishura
spellingShingle	Filipp Buryak Yuliya Mishura Convexity and robustness of the Rényi entropy Modern Stochastics: Theory and Applications Discrete distribution Rényi entropy convexity
author_facet	Filipp Buryak Yuliya Mishura
author_sort	Filipp Buryak
title	Convexity and robustness of the Rényi entropy
title_short	Convexity and robustness of the Rényi entropy
title_full	Convexity and robustness of the Rényi entropy
title_fullStr	Convexity and robustness of the Rényi entropy
title_full_unstemmed	Convexity and robustness of the Rényi entropy
title_sort	convexity and robustness of the rényi entropy
publisher	VTeX
series	Modern Stochastics: Theory and Applications
issn	2351-6046 2351-6054
publishDate	2021-07-01
description	We study convexity properties of the Rényi entropy as function of $\alpha >0$ on finite alphabets. We also describe robustness of the Rényi entropy on finite alphabets, and it turns out that the rate of respective convergence depends on initial alphabet. We establish convergence of the disturbed entropy when the initial distribution is uniform but the number of events increases to ∞ and prove that the limit of Rényi entropy of the binomial distribution is equal to Rényi entropy of the Poisson distribution.
topic	Discrete distribution Rényi entropy convexity
url	https://www.vmsta.org/doi/10.15559/21-VMSTA185
work_keys_str_mv	AT filippburyak convexityandrobustnessoftherenyientropy AT yuliyamishura convexityandrobustnessoftherenyientropy
_version_	1717379085464764416

Convexity and robustness of the Rényi entropy

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