Nearest-Neighbor and Contact Distance Distributions for Thomas Cluster\n Process

2016/09/26 by Mehrnaz Afshang, Afshang, Mehrnaz, Chiranjib Saha +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.1609.08137

Abstract

We characterize the statistics of nearest-neighbor and contact distance\ndistributions for Thomas cluster process (TCP), which is a special case of\nPoisson cluster process. In particular, we derive the cumulative distribution\nfunction (CDF) of the distance to the nearest point of TCP from a reference\npoint for three different cases: (i) reference point is not a part of the point\nprocess, (ii) it is chosen uniformly at random from the TCP, and (iii) it is a\nrandomly chosen point from a cluster chosen uniformly at random from the TCP.\nWhile the first corresponds to the contact distance distribution, the other two\nprovide two different viewpoints for the nearest-neighbor distance\ndistribution.\n

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