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A note on stochastic ordering of order statistics

Part of: Nonparametric inference Special processes

Published online by Cambridge University Press:  14 July 2016

Chunsheng Ma
Chunsheng Ma*
Affiliation:
University of Sydney
*
∗Postal address: School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia.
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Abstract

A necessary and sufficient condition is obtained for a Poisson binomial random variable to be stochastically larger (or smaller) than a binomial random variable. It is then used to deal with the stochastic comparisons of order statistics from heterogeneous populations with those from a homogeneous population. The result has obvious applications in the stochastic comparisons of lifetimes of k-out-of-n systems having independent components.

Keywords

HETEROGENEOUS SAMPLEHOMOGENEOUS SAMPLEK-OUT-OF-A2 SYSTEMPOISSON BINOMIAL DISTRIBUTIONORDER STATISTICSSTOCHASTIC ORDERING

MSC classification

Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 785 - 789
Copyright
Copyright © Applied Probability Trust 1997 

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References

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