Cauchy cluster process

In this paper we introduce an instance of the well-know Neyman–Scott cluster process model with clusters having a long tail behaviour. In our model the offspring points are distributed around the parent points according to a circular Cauchy distribution. Using a modified Cramér-von Misses test statistic and the simulated pointwise envelopes it is shown that this model fits better than the Thomas process to the frequently analyzed long-leaf pine data-set.