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A stochastic ordering of partial sums of independent random variables and of some random processes

Part of: Survival analysis and censored data Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Philip J. Boland ,
Frank Proschan  and
Y. L. Tong
Philip J. Boland*
Affiliation:
University College, Dublin
Frank Proschan*
Affiliation:
Florida State University
Y. L. Tong*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: Department of Statistics, University College Dublin, Belfield, Dublin 4, Ireland.
∗∗Postal address: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA.
∗∗∗Postal address: School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
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Abstract

In this paper we first prove an arrangement-decreasing property of partial sums of independent random variables when they are partially ordered through the likelihood ratio ordering. We then apply a similar argument to obtain a stochastic ordering of random processes via a comparison of their parameter functions, with special applications to Poisson and Wiener processes. Finally, in Section 4 we present some applications in reliability theory, queueing, and first-passage problems.

Keywords

ARRANGEMENT-DECREASING FUNCTIONSPOISSON PROCESSWIENER PROCESS

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992 , pp. 645 - 654
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research partially supported by AFOSR under Grant Nos 88–0040 and 89–0221.

Research partially supported by AFOSR under Grant Nos 88–0040 and 89–0221.

Research partially supported by the NSF under Grant No DMS-9001721.

References

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