Reduced Palm distribution generating function for a spatial point process

Abstract

The generating function of a marginal distribution of the reduced Palm distribution of a spatial point process is considered. It serves as a bivariate summary function, providing more information than some other popular univariate summary functions, such as the reduced second-moment function and the nearest-neighbour distance distribution function. Simulation confirmed that the new summary function is more informative when applied to patterns that exhibit both clustering and regularity on the same scale of observation.

Keywords:

• Generating function
• Reduced Palm distribution
• Spatial point process

Acknowledgements

This research was partially supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project Nos. HKBU2048/02P, HKBU200503, and HKBU200605) and a Faculty Research Grant of the Hong Kong Baptist University. I thank the referee and the associate editor for their valuable comments.