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Stochastic comparisons of order statistics under multivariate imperfect repair

Part of: Survival analysis and censored data Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

Taizhong Hu
Taizhong Hu*
Affiliation:
University of Science and Technology of China
*
∗Postal address: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
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Abstract

A monotone coupling of order statistics from two sets of independent non-negative random variables Xi, i = 1, ···, n, and Yi, i = 1, ···, n, means that there exist random variables X′i, Y′i, i = 1, ···, n, on a common probability space such that , and a.s. j = 1, ···, n, where X(1) ≦ X(2) ≦ ·· ·≦ X(n) are the order statistics of Xi, i = 1, ···, n (with the corresponding notations for the X′, Y, Y′ sample). In this paper, we study the monotone coupling of order statistics of lifetimes in two multi-unit systems under multivariate imperfect repair. Similar results for a special model due to Ross are also given.

Keywords

MONOTONE COUPLINGORDER STATISTICSSTOCHASTIC ORDERINGMULTIVARIATE IMPERFECT REPAIR

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 62G30: Order statistics; empirical distribution functions
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 156 - 163
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Research supported by a NNSF of China and a grant of Chinese Academy of Sciences.

References

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