Characterization of Partially Ordered Classes of Life Distributions.

摘要

In this paper we obtain characterizations of life distributions F such that 1/G(F) is convex (concave) and alternatively 1/G(F) is starshaped (antishaped), where G is an absolutely continuous life distribution with positive, bounded, right continuous density. These characterizations generalize earlier results for the IFR(DFR) and IFRA(DFRA) classes, and should prove useful in unifying the study of the class distributions with decreasing density, comparing Weibull (Gamma) distributions with different shape parameters, etc. (Author)