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Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions

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Abstract

Given a Poisson process in two or three dimensions, we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area. The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions. The accuracy of the approximation is checked through simulation.

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Authors and Affiliations

  1. Center for Safety Research, Royal Institute of Technology, Stockholm, Sweden

    Sven Erick Alm

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  1. Sven Erick Alm
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Alm, S.E. Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions. Extremes 1, 111–126 (1998). https://doi.org/10.1023/A:1009965918058

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