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Biometrika 1998 85(2):451-456; doi:10.1093/biomet/85.2.451
© 1998 by Biometrika Trust
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MISCELLANEA

Testing whether a survival distribution is new better than used of an unknown specified age

IBRAHIM A. AHMAD

Division of Statistics, Northern Illinois University DeKalb, Illinois 60115, U.S.A. ahmad{at}math.niu.edu

A survival variable is a nonnegative random variable X with distribution function F and a survival function This variable is said to be new better than used of specified age t0 if for all x ≥ 0 and a fixed t0. Testing for all x ≥ 0 against when the point to is unknown but can be estimated from the data is proposed when t0 = µ, the mean of F, and also when t0 = {xi}p, the pth percentile of F. It is shown that, while the known tests for known t0 (Hollander, Park & Proschan, 1986; Ebrahmi & Habibullah, 1990) continue to hold when t0 = µ and is estimated by , a simpler and distributionfree test is possible when t0 = {xi}p and is estimated by X([n,p]). The performance of this test is presented.

Key Words: Asymptotic normality • Estimated parameters • Percentiles • Pitman asymptotic efficiency • U-statistics


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