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Bivariate characterization of some stochastic order relations

Published online by Cambridge University Press:  01 July 2016

J. George Shanthikumar  and
David D. Yao
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
David D. Yao*
Affiliation:
Columbia University
*
∗Postal address: School of Business Administration, University of California, Berkeley, CA 94720, USA.
∗∗Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027-6699, USA.
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Abstract

Bivariate (and multivariate) functional representations for the following stochastic order relations are established: the likelihood ratio ordering, hazard rate ordering, and the usual stochastic ordering. The motivation of the study is (i) to provide a general approach that supports the ‘pairwise interchange' arguments widely used in various settings, and (ii) to develop new notions of stochastic order relations so that dependent random variables can be meaningfully compared. Applications are illustrated through problems in stochastic scheduling, closed queueing network and reliability.

Keywords

FUNCTIONAL REPRESENTATIONLIKELIHOOD RATIO ORDERINGHAZARD RATE ORDERINGSTOCHASTIC ORDERING
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 3 , September 1991 , pp. 642 - 659
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Supported in part by NSF under grant ECS-8811234.

The major part of this research was undertaken while David D. Yao was affiliated with the division of Applied Sciences, Harvard University. He has also been supported in part by NSF under grant ECS-88013183, and by ONR under contract N00014-84-K-0465.

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