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March, 1983 Testing Whether New is Better than Used with Randomly Censored Data
Yuan Yan Chen, Myles Hollander, Naftali A. Langberg
Ann. Statist. 11(1): 267-274 (March, 1983). DOI: 10.1214/aos/1176346077


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.


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Yuan Yan Chen. Myles Hollander. Naftali A. Langberg. "Testing Whether New is Better than Used with Randomly Censored Data." Ann. Statist. 11 (1) 267 - 274, March, 1983.


Published: March, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0504.62086
MathSciNet: MR684884
Digital Object Identifier: 10.1214/aos/1176346077

Primary: 62N05
Secondary: 62G10

Keywords: Classes of life distributions , efficiency loss , exponentiality

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 1 • March, 1983
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