Nearest Neighbor and Contact Distance Distribution for Binomial Point Process on Spherical Surfaces

Abstract

This letter characterizes the statistics of the contact distance and the nearest neighbor (NN) distance for binomial point processes (BPP) spatially-distributed on spherical surfaces. We consider a setup of n concentric spheres, with each sphere Sk has a radius rk and Nk points that are uniformly distributed on its surface. For that setup, we obtain the cumulative distribution function (CDF) of the distance to the nearest point from two types of observation points: (i) the observation point is not a part of the point process and located on a concentric sphere with a radius re