Department of Statistics, UCLA

This work presents an alternative derivation of the asymptotic distribution of Ripley's K-function for a homogeneous Poisson process and shows how it can be combined with point process residual analysis in order to test for different classes of point process models. This can be doen with the mean K-function of thinned residuals (K_M ) or a weighted analogue called the weighted or inhomogeneous K-function (K_W ). The asymptotic distributions of K_M and K_W are derived for inhomogeneous Poisson processes. Both statistics can be used as measures of goodness-of-fit for point process models.