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COMPARISONS OF SAMPLE RANGES ARISING FROM MULTIPLE-OUTLIER MODELS: IN MEMORY OF MOSHE SHAKED

Published online by Cambridge University Press:  29 December 2017

Narayanaswamy Balakrishnan ,
Jianbin Chen ,
Yiying Zhang  and
Peng Zhao
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Canada E-mail: bala@mcmaster.ca
Jianbin Chen
Affiliation:
LPMC and Institute of Statistics, Nankai University, Tianjin 300071, China E-mail: chenjianbinlzu@163.com
Yiying Zhang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China E-mail: zhyy@hku.hk
Peng Zhao
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China E-mail: zhaop@jsnu.edu.cn
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Abstract

In this paper, we discuss the ordering properties of sample ranges arising from multiple-outlier exponential and proportional hazard rate (PHR) models. The purpose of this paper is twofold. First, sufficient conditions on the parameter vectors are provided for the reversed hazard rate order and the usual stochastic order between the sample ranges arising from multiple-outlier exponential models with common sample size. Next, stochastic comparisons are separately carried out for sample ranges arising from multiple-outlier exponential and PHR models with different sample sizes as well as different hazard rates. Some numerical examples are also presented to illustrate the results established here.

Keywords

majorization ordermultiple-outlier models,PHR modelsp-larger orderreversed hazard rate ordersample rangeusual stochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 1 , January 2019 , pp. 28 - 49
Copyright
Copyright © Cambridge University Press 2017 

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