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A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process
Authors:Haiman  G  Preda  C
Institution:(1) UFR de Mathématiques, Université de Lille 1, 59655 Villeneuve drsquoAscq—, France;(2) LSTA Université, Paris, 6;(3) CERIM Dépt. de Statistique, Faculté de Médecine, Université de Lille 2, 1 Place de Verdun, 59045 Lille, France
Abstract:A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a ldquoperfect simulationrdquo algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.
Keywords:Poisson process  scan statistics  approximation
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