Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 2, 244--257

TESTING EXPONENTIALITY AGAINST POSITIVE AGEING USING KERNEL METHODS

By

IBRAHIM A. AHMAD, University of Central Florida, Orlando

SUMMARY. Using the very popular ``Kernel methods'' of curve fitting, a new approach is taken for testing exponentiality against some common positively aging life distributions such as the ``increasing failure'', the ``increasing failure rate average'', and the ``decreasing mean residual life''. The procedures presented here are shown to perform exceptionally well in the sense of Pitman's asymptotic relative efficiency relative to other procedures in the literature. Also, these procedures are shown, via simulation, to have excellent power for some common alternatives. Simulated small sample critical points of the tests are also given.

AMS (1991) subject classification. 62G05.

Key words and phrases. Life distributions, positive aging, IFR, IFRA, and DMRL life distributions, kernel, bandwidth, asymptotic normality, efficiency of tests, power of tests.

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