Moment-entropy inequalities for a random vector

Erwin Lutwak; Deane Yang; Gaoyong Zhang

doi:10.1109/TIT.2007.892780

Moment-entropy inequalities for a random vector

Erwin Lutwak, Deane Yang, Gaoyong Zhang

Mathematics

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

Abstract

The pth moment matrix is defined for a real random vector, generalizing the classical covariance matrix. Sharp inequalities relating the pth moment and Renyi entropy are established, generalizing the classical inequality relating the second moment and the Shannon entropy. The extremal distributions for these inequalities are completely characterized.

Original language	English (US)
Pages (from-to)	1603-1607
Number of pages	5
Journal	IEEE Transactions on Information Theory
Volume	53
Issue number	4
DOIs	https://doi.org/10.1109/TIT.2007.892780
State	Published - Apr 2007

Keywords

Covariance
Covariance matrix
Entropy
Information measure
Information theory
Moment
Moment matrix
Random vector
Renyi entropy

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2007.892780

Cite this

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abstract = "The pth moment matrix is defined for a real random vector, generalizing the classical covariance matrix. Sharp inequalities relating the pth moment and Renyi entropy are established, generalizing the classical inequality relating the second moment and the Shannon entropy. The extremal distributions for these inequalities are completely characterized.",

keywords = "Covariance, Covariance matrix, Entropy, Information measure, Information theory, Moment, Moment matrix, Random vector, Renyi entropy",

author = "Erwin Lutwak and Deane Yang and Gaoyong Zhang",

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AU - Yang, Deane

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AB - The pth moment matrix is defined for a real random vector, generalizing the classical covariance matrix. Sharp inequalities relating the pth moment and Renyi entropy are established, generalizing the classical inequality relating the second moment and the Shannon entropy. The extremal distributions for these inequalities are completely characterized.

KW - Covariance

KW - Covariance matrix

KW - Entropy

KW - Information measure

KW - Information theory

KW - Moment

KW - Moment matrix

KW - Random vector

KW - Renyi entropy

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Moment-entropy inequalities for a random vector

Abstract

Keywords

ASJC Scopus subject areas

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