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

被引：52
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 22 条
[1]  
[Anonymous], 2006, ESAIM Probab. Stat
[2]  
Bakry D., 1985, LECT NOTES MATH, V1123, P177, DOI DOI 10.1007/BFB0075847
[3]   ENTROPY AND THE CENTRAL-LIMIT-THEOREM [J].
BARRON, AR .
ANNALS OF PROBABILITY, 1986, 14 (01) :336-342
[4]   THE CONVOLUTION INEQUALITY FOR ENTROPY POWERS [J].
BLACHMAN, NM .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1965, 11 (02) :267-271
[5]   A NEW ENTROPY POWER INEQUALITY [J].
COSTA, MHM .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1985, 31 (06) :751-760
[6]  
EFRON B, 1965, ANN MATH STAT, V33, P272
[7]   Binomial and Poisson distributions as maximum entropy distributions [J].
Harremoës, P .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (05) :2039-2041
[8]   NEGATIVE ASSOCIATION OF RANDOM-VARIABLES, WITH APPLICATIONS [J].
JOAGDEV, K ;
PROSCHAN, F .
ANNALS OF STATISTICS, 1983, 11 (01) :286-295
[9]  
Johnstone I., 1987, SEMIN PROBABILITY, VXXI, P563
[10]  
Karlin S, 1968, TOTAL POSITIVITY
123