Poisson distribution

Statistics

Distribution (mathematics)

Operating system

k-nearest neighbors algorithm

Algorithm

Mathematical analysis

Artificial intelligence

Negative binomial distribution

Geometry

Binomial (polynomial)

Point (geometry)

Mathematics

Computer science

Binomial distribution

Point process

Process (computing)

IEEE Communications Letters

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 of 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.

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