Testing goodness-of-fit for the power law process
Exact goodness-of-fit tests for the power law process, a nonhomogeneous Poisson process with intensity function , can be constructed by making one of two transformations of the event times. The Kolmogorov-Smirnov, Cramer-von Mises or Anderson-Darling test can then be applied to these transformed variables. In this article it is shown that these two transformations lead to the same test statistics in one particular case. The results of a simulation study show that these tests have very low power when the alternative hypothesis is a renewal process. A transformation of these transformed variables, suggested by Durbin, increases the power substantially.