A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process

G. Haiman and C. Preda
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G. Haiman: Université de Lille 1
C. Preda: Université de Lille 2

Methodology and Computing in Applied Probability, 2002, vol. 4, issue 4, 393-407

Abstract: 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 “perfect simulation” algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.

Keywords: Poisson process; scan statistics; approximation (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (5)

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DOI: 10.1023/A:1023518602117

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