Testing whether a life distribution is new better than used in the tail

Abstract

A new class of life distributions, called new better than used of age t 0 and beyond (NBU-[t 0, ∞)), is introduced. It includes the class of new better than used (NBU) life distribution and is included in the class of new better than used of a specified age t 0(NBU − t 0). Testing whether a life distribution is exponential in [t 0, ∞) versus that it is NBU there is presented both when t 0 is known or when it is unknown but can be estimated. The special case when t 0 is the p-th percentile of the distribution leads to an asymptotically distribution-free procedure whether it is known or not.