Complete monotonicity of the entropy in the central limit theorem for gamma and inverse Gaussian distributions

被引：4

作者：

Yu, Yaming ^{[1
]}

机构：

[1] Univ Calif Irvine, Dept Stat, Irvine, CA 92697 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2009年 / 79卷 / 02期

关键词：

D O I：

10.1016/j.spl.2008.08.008

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：

Let be the differential entropy of the gamma distribution Gam(alpha, root alpha). It is shown that (1/2) log(2 pi e) - H(g) (alpha) is a completely monotone function of alpha. This refines the monotonicity of the entropy in the central limit theorem for gamma random variables. A similar result holds for the inverse Gaussian family. How generally this complete monotonicity holds is left as an open problem. (c) 2008 Elsevier B.V. All rights reserved.

引用

页码：270 / 274

页数：5

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