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 uniformity 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahrens, J. H. and Dieter, U. (1974). Non-uniform random numbers, Institute fur Math, Statistik, Technische Hochscule in Graz, Austria.
Chen, B., McCoskey, S. K. and Kao, C. (1999). Estimation and inference of a cointegrated regression in panel data: A Monte Carlo study, Amer. J. Math. Management Sci., 19, 75-114.
Cressie, N. (1976). On the logarithms of high-order spacings, Biometrika, 63, 343-355.
Dudewicz, E. and Ralley, T. G. (1981). The Handbook of Random Number Generation and Testing with TESTRAND Computer Code, American Sciences Press, Columbus, Ohio.
Dudewicz, E. and van der Meulen, E. (1981). Entropy based tests of uniformity, J. Amer. Statist. Assoc., 76, 967-974.
Dudewicz, E. and van der Meulen, E. (1984). On assessing the precision of simulation estimates of percentile points, Amer. J. Math. Management Sci., 114, 335-343.
Ebrahimi, N. (1996). How to measure uncertainty in the residual lifetime distribution, Sankhyā, Ser. A, 58, 48-57.
Ebrahimi, N. and Kirmani, S. N. U. A. (1996a). A characterization of the proportional hazards model through a measure of discrimination between two residual life distribution. Biometrika, 83, 233-235.
Ebrahimi, N. and Kirmani, S. N. U. A. (1996b). A measure of discrimination between two residual lifetime distributions and its applications, Ann. Inst. Statist. Math., 48, 257-265.
Ebrahimi, N., Habibulah, M. and Soofi, E. (1992). Testing exponentiality based on Kullback-Leibler information, J. Roy. Statist. Soc. Ser. B, 54, 739-748.
Ebrahimi, N., Pflughoft, K. and Soofi, E. S. (1994). Two measures of sample entropy, Statist. Probab. Lett., 20, 225-234.
Grubbs, F. E. (1971). Fiducial bounds on reliability for two parameter negative exponential distribution, Technometrics, 13, 873-876.
Karian, Z. A. and Dudewicz, E. (1999). Modern Statistical, Systems, and GPSS Simulation, 2ed., CRC Press, Boca Raton, Florida.
Stephens, M. A. (1974). EDF statistics for goodness of fit and some comparison, J. Amer. Statist. Assoc., 69, 730-737.
Vasicek, O. (1976). A test for normality based on simple entropy, J. Roy. Statist. Soc. Ser. B, 38, 54-59.
Author information
Authors and Affiliations
About this article
Cite this article
Ebrahimi, N. Testing for Uniformity of the Residual Life Time Based on Dynamic Kullback-Leibler Information. Annals of the Institute of Statistical Mathematics 53, 325–337 (2001). https://doi.org/10.1023/A:1012085320762
Issue Date:
DOI: https://doi.org/10.1023/A:1012085320762