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STOCHASTIC MONOTONICITY OF CONDITIONAL ORDER STATISTICS IN MULTIPLE-OUTLIER SCALE POPULATION

Published online by Cambridge University Press:  16 November 2016

Ebrahim Amini-Seresht  and
Yiying Zhang
Ebrahim Amini-Seresht
Affiliation:
Department of Statistics, Bu-Ali Sina University, Hamedan, Iran E-mail: [email protected]
Yiying Zhang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong E-mail: [email protected]
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Abstract

This paper discusses the stochastic monotonicity property of the conditional order statistics from independent multiple-outlier scale variables in terms of the likelihood ratio order. Let X1, …, Xn be a set of non-negative independent random variables with Xi, i=1, …, p, having common distribution function F(λ1x), and Xj, j=p+1, …, n, having common distribution function F(λ2x), where F(·) denotes the baseline distribution. Let Xi:n(p, q) be the ith smallest order statistics from this sample. Denote by $X_{i,n}^{s}(p,q)\doteq [X_{i:n}(p,q)|X_{i-1:n}(p,q)=s]$. Under the assumptions that xf′(x)/f(x) is decreasing in x∈ℛ+, λ1≤λ2 and s1≤s2, it is shown that $X_{i:n}^{s_{1}}(p+k,q-k)$ is larger than $X_{i:n}^{s_{2}}(p,q)$ according to the likelihood ratio order for any 2≤i≤n and k=1, 2, …, q. Some parametric families of distributions are also provided to illustrate the theoretical results.

Keywords

conditional order statisticslikelihood ratio orderpermanentrr2 dependent
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 3 , July 2017 , pp. 366 - 380
Copyright
Copyright © Cambridge University Press 2016 

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