kth distance distributions for generalized Gauss-Poisson process in Rn

For a point process (PP), the kth contact distance refers to the distance of kth closest point from an arbitrary location and the kth nearest neighbor distance refers to the distance of kth nearest neighbor from an arbitrary point of the PP. We consider the generalized n-dimensional Gauss-Poisson process and derive the closed-form expressions for the cumulative distribution functions (CDFs) of these two distances for the general k. We also validate our analysis via numerical simulations and provide various insights using the presented analysis. (C) 2021 Published by Elsevier B.V.

Automated summary

This study investigates the cumulative distribution functions of contact distance and nearest neighbor distance in a point process, deriving closed-form expressions for these distances in the generalized n-dimensional Gauss-Poisson process. The analysis is validated through numerical simulations, providing various insights into the characteristics of point processes.