Convexity and robustness of the Renyi entropy

被引：7

作者：

Buryak, Filipp ^{[1
]}

Mishura, Yuliya ^{[1
]}

机构：

[1] Kyiv Natl Taras Shevchenko Univ, Fac Mech & Math, Dept Probabil Theory Stat & Actuarial Math, Volodymyrska 64, UA-01601 Kiev, Ukraine

来源：

MODERN STOCHASTICS-THEORY AND APPLICATIONS | 2021年 / 8卷 / 03期

关键词：

Discrete distribution; Renyi entropy; convexity; DIVERGENCE;

D O I：

10.15559/21-VMSTA185

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study convexity properties of the Renyi entropy as function of alpha > 0 on finite alphabets. We also describe robustness of the Renyi 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 infinity and prove that the limit of Renyi entropy of the binomial distribution is equal to Renyi entropy of the Poisson distribution.

引用

页码：387 / 412

页数：26

共 16 条

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