Poisson limits for a clustering model of strauss
Roy Saunders, Gerald M. Funk · Journal of Applied Probability · 1977
In this article we present a limiting result for the random variable Y n ( r ) which arises in a clustering model of Strauss (1975). The result is that under some sparseness-of-points conditions the process { Y n ( 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.