Monte Carlo exact goodness-of-fit tests for nonhomogeneous Poisson processes

摘要

Nonhomogeneous Poisson processes (NHPPs) are often used to model failure data from repairable systems, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for parametric NHPPs. The idea is to use conditional tests given a sufficient statistic under the null hypothesis model. The tests are performed by simulating conditional samples given the sufficient statistic. Algorithms are presented for testing goodness-of-fit for the power law and the log-linear law NHPP models. It is noted that while exact algorithms for the power law case are well known in the literature, the availability of such algorithms for the log-linear case seems to be less known. A data example, as well as simulations, are considered.