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1 results

  • Poisson limits for a clustering model of strauss

  • Roy Saunders, Gerald M. Funk
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 4 / December 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 776-784
    Print publication:
    December 1977

  • 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.