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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]

A life distribution function (DF)Fis said to be star-shaped ifis nondecreasing on its support. This generalises the model of a convex DF, even allowing for jumps. The nonparametric maximum likelihood estimation is known to be inconsistent. We provide a uniformly strongly consistent least-squares estimator. We also derive the convergence in distribution of the estimator at a point whereis increasing using the arg max theorem. [ABSTRACT FROM AUTHOR]

The mean residual life of a non negative random variableXwith a finite mean is defined byM(t) =E[X−t|X>t] fort⩾ 0. A popular nonparametric model of aging is new better than used in expectation (NBUE), whenM(t) ⩽M(0) for allt⩾ 0. The exponential distribution lies at the boundary. There is a large literature on testing exponentiality against NBUE alternatives. However, comparisons of tests have been made only for alternatives much stronger than NBUE. We show that a new Kolmogorov-Smirnov type test is much more powerful than its competitors in most cases. [ABSTRACT FROM AUTHOR]

Relations, Bounds and Approximations for Order Statistics. Barry C. Arnold and N. Balakrishnan. New York: Springer-Verlag, 1989. ix + 173 pp. $20.60 (paperback). Approximate Distributions of Order Statistics: With Applications [...]

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]

Arnold Janssen and David M. Mason. New York: Springer-Verlag, 1990. vi + 252 pp. $34 (paperback). This monograph deals with asymptotic properties of rank tests under models where the Fisher [...]

Presents a study that examined an algorithm which utilizes elementary methods and requires no knowledge of linear programming. Information on the tests for independence or homogeneity in categorical data analysis; Development of convex polytopes; Background on the Bland's rule or the least subscript rule.

A study of the migration sequences of zinc and manganese, their separation from each other and from other ions such as Ni, Co, Ag, Cu, Pb, Bi, Hg and Cd in different electrolytes has been made. Zn and Mn ions from different binary, ternary and quaternary mixtures have been effectively separated and six cations from a mixture Pb-Co-Zn-Cd-Cu-Hg can be easily identified. Their complete separation is not possible under the conditions studied. [ABSTRACT FROM AUTHOR]