符合指数和熵的界限

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI:10.7153/MIA-2021-24-22

A. Acu, Gülen Başcanbaz-Tunca, I. Raşa

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引用次数: 3

摘要

。在本文中，我们考虑了离散概率分布的参数化族，并研究了与它们相关的R´enyi,Tsallis和Shannon熵。得到了这些熵的下界和上界，改进了文献中的一些结果。这些证明是基于经典分析、对偶锥理论和随机多数化理论的几种方法。R´enyi和Tsallis熵自然地用重合指数表示。因此，我们详细地研究了与相应的离散概率分布相关的符合指数。得到的结果直接引出了熵的性质。

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Bounds for indices of coincidence and entropies

. In this paper we consider a parameterized family of discrete probability distributions and investigate the R´enyi,Tsallis, and Shannon entropies associated with them. Lower and upper bounds for these entropies are obtained, improving some results from the literature. The proofs are based on several methods from classical analysis, theory of dual cones, and the stochastic majorization theory. The R´enyi and Tsallis entropies are naturally expressed in terms of the index of coincidence. Consequently we study in detail the index of coincidence associated to the corresponding discrete probability distributions. The obtained results lead immediately to properties of the entropies.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.