Journal of Applied Probability

On the skewness of order statistics in multiple-outlier models

Subhash Kochar and Maochao Xu

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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.

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J. Appl. Probab., Volume 48, Number 1 (2011), 271-284.

First available in Project Euclid: 15 March 2011

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings 62N05: Reliability and life testing [See also 90B25] 62G30: Order statistics; empirical distribution functions 62D05: Sampling theory, sample surveys

Dispersive order exponential distribution decreasing failure rate k-out-of-n system proportional hazard rate right spread order skewness star order


Kochar, Subhash; Xu, Maochao. On the skewness of order statistics in multiple-outlier models. J. Appl. Probab. 48 (2011), no. 1, 271--284. doi:10.1239/jap/1300198149.

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