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 ≦ r ≦ r∞} converges weakly to a non-homogeneous Poisson process {Y(r): 0 ≦ r ≦ r∞} 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 Unpublished technical report.
Cited by
31 articles.
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