GOODNESS-OF-FIT TEST FOR POISSON PROCESSES WITH A SCALE PARAMETER

We propose the goodness-of-fit test for inhomogeneous Poisson processes with unknown scale parameter. A test statistic of the Anderson-Darling type is proposed and its asymptotic behavior is studied when the unknown parameter is estimated using the maximum likelihood estimator. We show that under null hypothesis, the limit distribution of this statistic does not depend on unknown parameter. Furthermore, we establish the consistency of the test against the alternative hypothesis.