TESTING FOR UNIFORMITY OF THE RESIDUAL LIFE TIME BASED ON DYNAMIC KULLBACK-LEIBLER INFORMATION

NADER EBRAHIMI

Division of Statistics, Northern Illinois University, DeKalb, IL 60115-2854, U.S.A.

(Received July 1, 1997; revised March 6, 2000)

Abstract. In this article a goodness of fit test for distributional assumptions regarding the residual lifetime is proposed. The test is based on a Vasicek type sum log-spacings estimators of a dynamic version of Kullback-Leibler information. The specific distributional hypothesis considered is of the unformity over [0,1]. However, the test can be used for testing any simple goodness of fit hypothesis. The asymptotic distribution of the test statistic together with a tabulation of the critical points for different sample sizes are given. Finally, the power function of the test is empirically studied in comparison with some competitors, and the test appears to be meritorious.

Key words and phrases: Discrimination information, uniformity tests, goodness-of-fit tests, consistent tests.