## The Annals of Statistics

### On Testing Whether New is Better Than Used Using Randomly Censored Data

Yoshiki Kumazawa

#### Abstract

Under a model of random censorship, we consider the test $H_0$: a life distribution is exponential, versus $H_1$: it is new better than used, but not exponential. This paper introduces a class of tests by using the Kaplan-Meier estimator for the sample distribution in the uncensored model. Under some regularity conditions, the asymptotic normality of statistics is derived by an application of von Mises' method, and asymptotically valid tests are obtained by using estimators for the null standard deviations. The efficiency loss in the proportional censoring model is studied and a Monte Carlo study of power is performed.

#### Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 420-426.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350276

Digital Object Identifier
doi:10.1214/aos/1176350276

Mathematical Reviews number (MathSciNet)
MR885747

Zentralblatt MATH identifier
0613.62123

JSTOR