Neyman-Scott process with skew-normal clusters

In the real world, there are point patterns where the offspring points are asymmetrically scattered around the parent points and have skewness in their locations. However, the existing distributions for the offspring locations in Neyman-Scott processes are usually assumed to be without any skewness in the clusters. This paper introduces a generalization of the Thomas process where the offspring points have a skew-normal distribution. We derive the pair correlation and third order intensity reweighted product density functions for the proposed process and use the composite likelihood approach to estimate the parameters. The model is applied to three real data sets and using the envelopes test and the DCLF test it is shown that the model provides a better fit than the ordinary Thomas process to the data.