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Biometrika 1990 77(1):212-215;
© 1990 by Biometrika Trust
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MISCELLANEA

Testing whether the survival distribution is new better than used of specified age

NADER EBRAHIMI and MOHAMED HABIBULLAH

Department of Mathematical Sciences, Division of Statistics, Northern Illinois University DeKalb, Illinois 60115, U.S.A.
Division of Sciences and Mathematics, University of Wisconsin-Superior Superior, Wisconsin 54880, U.S.A.

Received for publication 1 May 1988. Revision received 1 March 1989.
  Abstract

The cumulative distribution function F, of a nonnegative random variable, is said to be new better than used of specified age t0 if Formula for all Formula, where FormulaLet


Formula

We propose a class of test statistics Tk, indexed by a positive integer k, for testing the null hypothesis that F belongs to A against the alternative hypothesis that F is new better than used of specified age t0 but not in A. We compare the performance of our proposed test statistics with the test given by Hollander, Park & Proschan (1986). The proposed tests perform better than their test for some alternatives.

Key Words: Pitman efficiency • U-statistic


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