## The Annals of Statistics

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

### Distribution-Free Tolerance Intervals for Stochastically Ordered Distributions

#### 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