Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T17:04:51.717Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on stochastic ordering of order statistics

Part of: Special processes Nonparametric inference

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ball, F. (1985) Deterministic and stochastic epidemics with several kinds of susceptibles. Adv. Appl. Prob. 17, 1–22.Google Scholar
Barbour, A. D., Lindvall, T. and Rogers, L. C. G. (1991) Stochastic ordering of order statistics. J. Appl. Prob. 28, 278–286.Google Scholar
Hoeffding, W. (1956) On the distribution of the number of successes in independent trials. Ann. Math. Statist. 27, 713–721.Google Scholar
Li, H. and Shared, M. (1993) Stochastic majorization of stochastically monotone families of random variables. Adv. Appl. Prob. 25, 895–913.Google Scholar
Pledger, G. and Proschan, F. (1971) Comparisons of order statistics and of spacing from heterogeneous distributions. In Optimizing Methods in Statistics. ed. Rustagi, J. S. Academic Press, New York.Google Scholar
Proschan, F. and Sethuraman, J. (1976) Stochastic comparison of order statistics from heterogeneous populations, with applications in reliability. J. Multivar. Anal. 6, 608–616.Google Scholar
Sen, P. K. (1970) A note on order statistics for heterogeneous distributions. Ann. Math. Statist. 41, 2137–2139.Google Scholar