Log-concavity and the maximum entropy property of the Poisson distribution

被引：51
|
作者：
Johnson, Oliver [1 ]
机构：
[1] Univ Cambridge, Ctr Math Sci, Stat Lab, Cambridge CB3 0WB, England
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2007年 / 117卷 / 06期
关键词：
log-concavity; maximum entropy; Poisson distribution; thinning; ultra log-concavity;
D O I：
10.1016/j.spa.2006.10.006
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 prove that the Poisson distribution maximises entropy in the class of ultra log-concave distributions, extending a result of Harremoes. The proof uses ideas concerning log-concavity, and a semigroup action involving adding Poisson variables and thinning. We go on to show that the entropy is a concave function along this semigroup. (C) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码：791 / 802
页数：12
相关论文
共 50 条
12345