Large Sample Tests for the Monotonicity of a Generalized Failure Rate Function

摘要

The generalized failure rate function of a distribution function F(density f) with respect to a distribution function G (density g) is f(x)/ gG sup(-1) (F(x)), for x such that O>F(x)>1. Given a distribution function G and a random sample from a distribution function F the author considers tests of the null hypothesis that the generalized failure rate function of F with respect to G is constant against alternatives where the generalized failure rate is increasing. The tests, which are based on studentized linear spacings statistics, are shown to satisfy optimum properties when the distribution function G puts all of its mass on a finite interval. (Author)