Convexity and robustness of the Rényi entropy
Open Access
- 26 July 2021
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 8 (3), 387-412
- https://doi.org/10.15559/21-vmsta185
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Convexity and robustness of the Rényi entropy, Authors: Filipp Buryak, Yuliya Mishura , 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.
Keywords
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