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Comparisons of Parallel Systems According to the Convex Transform Order

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

Published online by Cambridge University Press:  14 July 2016

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

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A parallel system with heterogeneous exponential component lifetimes is shown to be more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. As a consequence, equivalent conditions for comparing the variabilities of the largest order statistics from heterogeneous and homogeneous exponential samples in the sense of the dispersive order and the right-spread order are established. A sufficient condition is also given for the proportional hazard rate model.

Keywords

Convex transform orderexponential distributionincreasing failure rateparallel system; proportional hazard rateright-spread orderskewness

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 46 , Issue 2 , June 2009 , pp. 342 - 352
Copyright
Copyright © Applied Probability Trust 2009 

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