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Entropy inequalities for classes of probability distributions II. The multivariate case

Published online by Cambridge University Press:  01 July 2016

Samuel Karlin  and
Yosef Rinott
Samuel Karlin*
Affiliation:
Stanford University
Yosef Rinott*
Affiliation:
Stanford University
*
∗Postal adress: Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A.
∗Postal adress: Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A.
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Abstract

In this paper we continue our investigation of entropy comparisons with emphasis on multivariate distributions. For multiparameter cases of the multinomial and negative multinomial distributions we consider various higher-order forms of multivariate convexity. For the multinormal, Wishart, and t-distributions we define a partial ordering on the set of covariance matrices and determine monotonicity of the entropy functional. We further indicate some entropy inequalities for different sampling schemes. Because of the complex nature of multivariate partial ordering relations several problems remain open.

Keywords

ENTROPY FUNCTIONALMULTIVARIATE DISTRIBUTIONSMULTIVARIATE SCHUR CONVEXITY
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 2 , June 1981 , pp. 325 - 351
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

Yosef Rinott is also a member of the Department of Statistics, The Hebrew University, Jerusalem, Israel.

Supported in part by NIH Grant 2R01 GM10452–16 and NSF Grant MCS76–80624-A02.

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