A new test for decreasing mean residual lifetimes

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Authors
Lorenzo, Edgardo
Malla, Ganesh B.
Mukerjee, Hari
Issue Date
2018-03-02
Type
Article
Language
en_US
Keywords
Asymptotic properties , Decreasing mean residual life , Hypothesis test , Sup-test
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Abstract

The mean residual life of a non negative random variable X with a finite mean is defined by M(t) = E[X - t|X > t] for t 0. One model of aging is the decreasing mean residual life (DMRL): M is decreasing (non increasing) in time. It vastly generalizes the more stringent model of increasing failure rate (IFR). The exponential distribution lies at the boundary of both of these classes. There is a large literature on testing exponentiality against DMRL alternatives which are all of the integral type. Because most parametric families of DMRL distributions are IFR, their relative merits have been compared only at some IFR alternatives. We introduce a new Kolmogorov-Smirnov type sup-test and derive its asymptotic properties. We compare the powers of this test with some integral tests by simulations using a class of DMRL, but not IFR alternatives, as well as some popular IFR alternatives. The results show that the sup-test is much more powerful than the integral tests in all cases.

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Citation
Lorenzo, Edgardo; Malla, Ganesh B.; Mukerjee, Hari. 2018. A new test for decreasing mean residual lifetimes. Communications in Statistics - Theory and Methods. vol. 47:no. 12:pp 2805-2812
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Taylor & Francis
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ISSN
0361-0926
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