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July, 1987 Majorization, Randomness and Dependence for Multivariate Distributions
Harry Joe
Ann. Probab. 15(3): 1217-1225 (July, 1987). DOI: 10.1214/aop/1176992093

Abstract

The preorder relation of Hardy, Littlewood and Polya (1929), Day (1973) and Chong (1974, 1976) is applied to multivariate probability densities. This preorder, which is called majorization here, can be interpreted as an ordering of randomness. When used to compare multivariate densities with the same marginal densities, it can be interpreted as an ordering of dependence or conditional dependence. Results in Hickey (1983, 1984) and Joe (1985) are generalized. A relative entropy function is proposed as a measure of dependence or conditional dependence for multivariate densities with the same marginals.

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Harry Joe. "Majorization, Randomness and Dependence for Multivariate Distributions." Ann. Probab. 15 (3) 1217 - 1225, July, 1987. https://doi.org/10.1214/aop/1176992093

Information

Published: July, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0657.60022
MathSciNet: MR893926
Digital Object Identifier: 10.1214/aop/1176992093

Subjects:
Primary: 62H20
Secondary: 62H99

Keywords: Entropy , majorization , ordering of dependence

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • July, 1987
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