Poisson limits for a clustering model of strauss

Author:

Saunders Roy,Funk Gerald M.

Abstract

In this article we present a limiting result for the random variable Yn(r) which arises in a clustering model of Strauss (1975). The result is that under some sparseness-of-points conditions the process {Yn(r): 0 ≦ rr} converges weakly to a non-homogeneous Poisson process {Y(r): 0 ≦ rr} when n → ∞. Simulation results are given to indicate the accuracy of the approximation when n is moderate and applications of the limiting result to tests for clustering are discussed.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference5 articles.

1. The Supremum and Infimum of the Poisson Process

2. A model for clustering

3. A note on Strauss's model for clustering

4. Saunders R. and Funk G. M. (1976) Convergence of a process arising in a clustering model. Unpublished technical report.

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