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November, 1976 Distribution-Free Tolerance Intervals for Stochastically Ordered Distributions
K. M. Lal Saxena
Ann. Statist. 4(6): 1210-1218 (November, 1976). DOI: 10.1214/aos/1176343652


Consider $k$ stochastically ordered distributions with $F_{(1)} \leqq\cdots\leqq F_{(k)}$. The present paper deals with distribution-free tolerance intervals for $F_{(j)}$ based on order statistics in samples of same size from each of the $k$ distributions. Two criteria are defined for determining such intervals. These two criteria are extensions of $\beta$-expectation tolerance intervals and $\beta$-content tolerance intervals with confidence coefficient $\gamma$ used in the single population literature. A tolerance interval for the lifetime distribution of a series system is considered as an example.


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K. M. Lal Saxena. "Distribution-Free Tolerance Intervals for Stochastically Ordered Distributions." Ann. Statist. 4 (6) 1210 - 1218, November, 1976.


Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0371.62065
MathSciNet: MR431510
Digital Object Identifier: 10.1214/aos/1176343652

Primary: 62G15
Secondary: 62G30 , 62N05

Keywords: Beta distributions , distribution-free , order statistics , reliability and life testing , stochastically ordered family , tolerance intervals

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 6 • November, 1976
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