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Stochastic comparisons of random minima and maxima

Part of: Special processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Moshe Shaked  and
Tityik Wong
Moshe Shaked*
Affiliation:
University of Arizona
Tityik Wong*
Affiliation:
Community College of Southern Nevada
*
∗Postal address: Department of Mathematics, Building #89, University of Arizona, Tucson, Arizona 85721, USA.
∗∗Postal address: Department of Mathematics, Community College of Southern Nevada, 3200 E. Cheyenne Ave-S1A, North Las Vegas, Nevada 89030, USA.
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Abstract

Let X1, X2,… be a sequence of independent random variables and let N be a positive integer-valued random variable which is independent of the Xi. In this paper we obtain some stochastic comparison results involving min {X1, X2,…, XN) and max{X1, X2,…, XN}.

Keywords

HAZARD RATE ORDERREVERSE HAZARD RATE ORDERLIKELIHOOD RATIO ORDERUSUAL STOCHASTIC ORDERLAPLACE TRANSFORMLAPLACE TRANSFORM ORDERRANDOM MINIMA AND MAXIMARELIABILITY THEORY

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 420 - 425
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Supported by NSF Grant DMS 9303891.

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