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A Note on Conditioning and Stochastic Domination for Order Statistics
Published online by Cambridge University Press: 14 July 2016
Abstract
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).
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- 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.
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