Information-theoretic inequalities for contoured probability distributions

被引：29

作者：

Guleryuz, OG

Lutwak, E

Yang, D

Zhang, GY

机构：

[1] Polytech Univ, Dept Elect Engn, Brooklyn, NY 11201 USA

[2] Polytech Univ, Dept Math, Brooklyn, NY 11201 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2002年 / 48卷 / 08期

关键词：

Brunn-Minkowski; convex bodies; elliptically contoured; entropy; Fisher information; inequalities; isoperimetric inequalities;

D O I：

10.1109/TIT.2002.800496

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy., We also obtain a new reverse information-theoretic inequality for contoured distributions.

引用

页码：2377 / 2383

页数：7

共 20 条

[1] On sharp Sobolev embedding and the logarithmic Sobolev inequality [J].