Neyman-Scott process with skew-normal clusters

Abstract

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.

Keywords:

• Composite likelihood approach
• DCLF test
• envelopes test
• offspring
• parent
• Thomas process

Acknowledgments

We would like to thank to the anonymous referees for their helpful comments. The authors also are grateful to Professor A. Baddeley for his great pieces of advice on R codes in finding close triples of points. The BCI forest dynamics research project was made possible by National Science Foundation grants to Stephen P. Hubbell: DEB-0640386, DEB-0425651, DEB-0346488, DEB-0129874, DEB-00753102, DEB-9909347, DEB-9615226, DEB-9615226, DEB-9405933, DEB-9221033, DEB-9100058, DEB-8906869, DEB-8605042, DEB-8206992, DEB-7922197, support from the Center for Tropical Forest Science, the Smithsonian Tropical Research Institute, the John D. and Catherine T. MacArthur Foundation, the Mellon Foundation, the Small World Institute Fund, and numerous private individuals, and through the hard work of over 100 people from 10 countries over the past two decades. The plot project is part the Center for Tropical Forest Science, a global network of large-scale demographic tree plots.