Information-theoretic inequalities for contoured probability distributions

Onur G. Guleryuz; Erwin Lutwak; Deane Yang; Gaoyong Zhang

doi:10.1109/TIT.2002.800496

Information-theoretic inequalities for contoured probability distributions

Onur G. Guleryuz, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Mathematics

Research output: Contribution to journal › Letter › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	2377-2383
Number of pages	7
Journal	IEEE Transactions on Information Theory
Volume	48
Issue number	8
DOIs	https://doi.org/10.1109/TIT.2002.800496
State	Published - Aug 2002

Keywords

Brunn-Minkowski
Convex bodies
Elliptically contoured
Entropy
Fisher information
Inequalities
Isoperimetric inequalities

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2002.800496

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abstract = "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.",

keywords = "Brunn-Minkowski, Convex bodies, Elliptically contoured, Entropy, Fisher information, Inequalities, Isoperimetric inequalities",

author = "Guleryuz, {Onur G.} and Erwin Lutwak and Deane Yang and Gaoyong Zhang",

year = "2002",

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T1 - Information-theoretic inequalities for contoured probability distributions

AU - Guleryuz, Onur G.

AU - Lutwak, Erwin

AU - Yang, Deane

AU - Zhang, Gaoyong

PY - 2002/8

Y1 - 2002/8

N2 - 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.

AB - 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.

KW - Brunn-Minkowski

KW - Convex bodies

KW - Elliptically contoured

KW - Entropy

KW - Fisher information

KW - Inequalities

KW - Isoperimetric inequalities

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M3 - Letter

AN - SCOPUS:0036671994

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EP - 2383

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 8

ER -

Information-theoretic inequalities for contoured probability distributions

Abstract

Keywords

ASJC Scopus subject areas

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