English

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}
}
R2 v1 2026-06-22T16:01:57.407Z