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

05/15/2020

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by   Anna Talgat, et al.

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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 S_k has a radius r_k and N_k 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 o observation points: (i) the observation point is not a part of the point process and located on a concentric sphere with a radius r_e<r_k∀ k, which corresponds to the contact distance distribution, and (ii) the observation point belongs to the point process, which corresponds to the nearest-neighbor (NN) distance distribution.