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Likelihood ratio order of parallel systems with...
Journal article

Likelihood ratio order of parallel systems with heterogeneous Weibull components

Abstract

In this paper, we compare the largest order statistics arising from independent heterogeneous Weibull random variables based on the likelihood ratio order. Let X1,…,Xn$$X_{1},\ldots ,X_{n}$$ be independent Weibull random variables with Xi$$X_{i}$$ having shape parameter 0<α≤1$$0<\alpha \le 1$$ and scale parameter λi$$\lambda _{i}$$, i=1,…,n$$i=1,\ldots ,n$$, and Y1,…,Yn$$Y_{1},\ldots ,Y_{n}$$ be a random sample of size n from a Weibull distribution with shape parameter 0<α≤1$$0<\alpha \le 1$$ and a common scale parameter λ¯=1n∑i=1nλi$$\overline{\lambda }=\frac{1}{n}\sum \nolimits _{i=1}^{n}\lambda _{i}$$, the arithmetic mean of λi′s$$\lambda _{i}^{'}s$$. Let Xn:n$$X_{n:n}$$ and Yn:n$$Y_{n:n}$$ denote the corresponding largest order statistics, respectively. We then prove that Xn:n$$X_{n:n}$$ is stochastically larger than Yn:n$$Y_{n:n}$$ in terms of the likelihood ratio order, and provide numerical examples to illustrate the results established here.

Authors

Fang L; Balakrishnan N

Journal

Metrika, Vol. 79, No. 6, pp. 693–703

Publisher

Springer Nature

Publication Date

August 1, 2016

DOI

10.1007/s00184-015-0573-5

ISSN

0026-1335

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