The Annals of Statistics

Distribution-Free Tolerance Intervals for Stochastically Ordered Distributions

K. M. Lal Saxena

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 4, Number 6 (1976), 1210-1218.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343652

Digital Object Identifier
doi:10.1214/aos/1176343652

Mathematical Reviews number (MathSciNet)
MR431510

Zentralblatt MATH identifier
0371.62065

JSTOR
links.jstor.org

Subjects
Primary: 62G15: Tolerance and confidence regions
Secondary: 62G30: Order statistics; empirical distribution functions 62N05: Reliability and life testing [See also 90B25]

Keywords
Distribution-free tolerance intervals stochastically ordered family order statistics beta distributions reliability and life testing

Citation

Saxena, K. M. Lal. Distribution-Free Tolerance Intervals for Stochastically Ordered Distributions. Ann. Statist. 4 (1976), no. 6, 1210--1218. doi:10.1214/aos/1176343652. https://projecteuclid.org/euclid.aos/1176343652


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