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The mean residual life of a life distribution,X, with a finite mean is defined byM(t) =E[X−tX>t] fort⩾ 0. Kochar et al. (2000) provided an estimator ofMwhen it is assumed to be decreasing. They showed that its asymptotic distribution was the same as that of the empirical estimate, but only under very stringent analytic and distributional assumptions. We provide a more general asymptotic theory, and under much weaker conditions. We also provide improved asymptotic confidence bands. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]