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.

Key words:

Poisson process, scan statistic, approximation

Research supported by the Axel and Margaret Ax:son Johnson Foundation.
1998-04-06, Sven Erick Alm,