Real-time prequential goodness-of-fit testing of life distributions in renewal processes

Abstract

Abstract The paper presents an omnibus goodness-of-fit (Gof) test for renewal processes based on Dawid’s prequential framework. This test compares models on the basis of their predictive abilities. It uses usual Edf statistics (KS, AD or CvM) of a prequential empirical process which, under standard regulatory conditions, is proven to converge to the Brownian bridge as in the case of known parameters. This result gives an asymptotically distribution free and computationally-simple Gof test. It can be used as a model-checking tool particularly adapted to sequential (or real-time) analysis of reliability or medical lifetimes data modelled by renewal processes. The prequential Gof test still probably valid for more complex models beyond the renewal framework.