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Stochastic majorization of stochastically monotone families of random variables

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  01 July 2016

Haijun Li  and
Moshe Shaked
Haijun Li*
Affiliation:
University of Arizona
Moshe Shaked*
Affiliation:
University of Arizona
*
* Postal address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA. Research supported by AFOSR Grant AFOSR-90–0201.
* Postal address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA. Research supported by AFOSR Grant AFOSR-90–0201.
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Abstract

Stochastic majorization is a tool that has been used in many areas of probability and statistics (such as multivariate statistical analysis, queueing theory and reliability theory) in order to obtain useful bounds and inequalities. In this paper we study the relations among several notions of stochastic majorization and stochastic convexity and obtain sufficient (and sometimes necessary) conditions which imply some of these notions. Extensions and generalizations of several results in the literature are obtained. Some examples and applications regarding stochastic comparisons of order statistics are also presented in order to illustrate the results of the paper.

Keywords

STOCHASTIC ORDERINGSEMIGROUP PROPERTIESSTOCHASTIC CONVEXITY AND CONCAVITYSTOCHASTIC SCHUR CONVEXITYLOGCONVEXITY AND LOGCONCAVITYRELIABILITY THEORYHAZARD RATE ORDERINGSUBMODULAR AND SUPERMODULAR FUNCTIONSORDER STATISTICSOPTIMAL ALLOCATIONSLIKELIHOOD RATIO ORDERING

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 4 , December 1993 , pp. 895 - 913
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research supported by AFOSR Grant AFOSR-90-0201.

Reproduction in whole or in part is permitted for any purpose by the United States Government.

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