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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: e.amini64@yahoo.com
Yiying Zhang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong E-mail: zhyy@hku.hk
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Abstract

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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 X 1, …, X n be a set of non-negative independent random variables with X i , i=1, …, p, having common distribution function F(λ1x), and X j , j=p+1, …, n, having common distribution function F(λ2x), where F(·) denotes the baseline distribution. Let X i: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 s 1≤s 2, 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 orderpermanentrr 2 dependent

Information

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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