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On the Skewness of Order Statistics in Multiple-Outlier Models

Part of: Survival analysis and censored data Nonparametric inference Sampling theory, sample surveys Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Subhash Kochar  and
Maochao Xu
Subhash Kochar*
Affiliation:
Portland State University
Maochao Xu*
Affiliation:
Illinois State University
*
∗Postal address: Department of Mathematics and Statistics, Portland State University, Portland, Oregon 97201, USA.
∗∗Postal address: Department of Mathematics, Illinois State University, Normal, Illinois 61790-4520, USA. Email address: [email protected]
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Abstract

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Kochar and Xu (2009) proved that a parallel system with heterogeneous exponential component lifetimes is more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. In this paper we extend this study to the general k-out-of-n systems for the case when there are only two types of component in the system. An open problem proposed in Pǎltǎnea (2008) is partially solved.

Keywords

Dispersive orderexponential distributiondecreasing failure ratek-out-of-n systemproportional hazard rateright spread orderskewnessstar order

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 62N05: Reliability and life testing 62G30: Order statistics; empirical distribution functions 62D05: Sampling theory, sample surveys
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 271 - 284
Copyright
Copyright © Applied Probability Trust 2011 

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