Approximation and Simulation of the Distributions of Scan Statistics for
Poisson Processes in Higher Dimensions
Sven Erick Alm
Center for Safety Research, Royal Institute of Technology
In Extremes 1:1, 111-126 (1998)
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 can be extended to higher dimensions.
In two dimensions, reasonable approximations for non-rectangular scanning sets
are also obtained using a simple correction of the rectangular result.
Poisson process, scan statistic, approximation
Research supported by the Axel and Margaret Ax:son Johnson Foundation.