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A Note on Conditioning and Stochastic Domination for Order Statistics

Part of: Distribution theory - Probability Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

Devdatt Dubhashi  and
Olle Häggström
Devdatt Dubhashi*
Affiliation:
Chalmers University of Technology
Olle Häggström*
Affiliation:
Chalmers University of Technology
*
∗Postal address: Department of Computing Science, Chalmers University of Technology, S-412 96 Göteborg, Sweden.
∗∗Postal address: Department of Mathematicical Statistics, Chalmers University of Technology, S-412 96 Göteborg, Sweden. Email address: olleh@math.chalmers.se
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Abstract

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For an order statistic (X1:n,…,Xn:n) of a collection of independent but not necessarily identically distributed random variables, and any i ∈ {1,…,n}, the conditional distribution of (Xi+1:n,…,Xn:n) given Xi:n > s is shown to be stochastically increasing in s. This answers a question by Hu and Xie (2006).

Keywords

Order statisticscouplingstochastic domination

MSC classification

Secondary: 62G30: Order statistics; empirical distribution functions 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 575 - 579
Copyright
Copyright © Applied Probability Trust 2008 

Footnotes

Supported by the Swedish Research Council and by the G-ran Gustafsson Foundation for Research in the Natural Sciences and Medicine.

References

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