The Annals of Statistics

Testing Whether New is Better than Used with Randomly Censored Data

Yuan Yan Chen, Myles Hollander, and Naftali A. Langberg

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Abstract

A life distribution $F$, with survival function $\bar{F} \equiv 1 - F$, is new better than used (NBU) if $\bar{F}(x + y) \leq \bar{F}(x)\bar{F}(y)$ for all $x, y \geq 0$. We propose a test of $H_0 : F$ is exponential, versus $H_1 : F$ is NBU, but not exponential, based on a randomly censored sample of size $n$ from $F$. Our test statistic is $J^c_n = \int \int \bar{F}_n(x + y) dF_n(x) dF_n(y)$, where $F_n$ is the Kaplan-Meier estimator. Under mild regularity on the amount of censoring, the asymptotic normality of $J^c_n$, suitably normalized, is established. Then using a consistent estimator of the null standard deviation of $n^{1/2}J^c_n$, an asymptotically exact test is obtained. We also study, using tests for the censored and uncensored models, the efficiency loss due to the presence of censoring.

Article information

Source
Ann. Statist., Volume 11, Number 1 (1983), 267-274.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346077

Digital Object Identifier
doi:10.1214/aos/1176346077

Mathematical Reviews number (MathSciNet)
MR684884

Zentralblatt MATH identifier
0504.62086

JSTOR
links.jstor.org

Subjects
Primary: 62N05: Reliability and life testing [See also 90B25]
Secondary: 62G10: Hypothesis testing

Keywords
Classes of life distributions efficiency loss exponentiality

Citation

Chen, Yuan Yan; Hollander, Myles; Langberg, Naftali A. Testing Whether New is Better than Used with Randomly Censored Data. Ann. Statist. 11 (1983), no. 1, 267--274. doi:10.1214/aos/1176346077. https://projecteuclid.org/euclid.aos/1176346077


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Corrections

  • See Correction: Yuan Yan Chen, Myles Hollander, Naftali A. Langberg. Corrections: Testing Whether New is Better than Used with Randomly Censored Data. Ann. Statist., Volume 11, Number 4 (1983), 1267--1267.