Nearest-Neighbor and Contact Distance Distributions for Thomas Cluster Process
Information Theory
2016-09-27 v1 math.IT
Abstract
We characterize the statistics of nearest-neighbor and contact distance distributions for Thomas cluster process (TCP), which is a special case of Poisson cluster process. In particular, we derive the cumulative distribution function (CDF) of the distance to the nearest point of TCP from a reference point for three different cases: (i) reference point is not a part of the point process, (ii) it is chosen uniformly at random from the TCP, and (iii) it is a randomly chosen point from a cluster chosen uniformly at random from the TCP. While the first corresponds to the contact distance distribution, the other two provide two different viewpoints for the nearest-neighbor distance distribution.
Cite
@article{arxiv.1609.08137,
title = {Nearest-Neighbor and Contact Distance Distributions for Thomas Cluster Process},
author = {Mehrnaz Afshang and Chiranjib Saha and Harpreet S. Dhillon},
journal= {arXiv preprint arXiv:1609.08137},
year = {2016}
}