Approximations of the distributions of scan statistics of Poisson processes


Sven Erick Alm

Uppsala University, Dept. of Mathematics

In Scan Statistics and Applications, Eds Glaz&Balakrishnan, Birkhäuser (1999)


We study scan statistics of Poisson processes in one and higher dimensions. First, a very accurate approximation is established in one dimension. This is done by studying upcrossings of the scanning process and noting that these occur in clusters. The clusters appear more or less independently and the cluster size is estimated by a random walk argument. This idea is then used repeatedly to obtain approximations in higher dimensions. Simulation is used to check the accuracy of the approximations in two and three dimensions. A discussion of these simulations is included, as they are by no means trivial to perform.

Key words:

Scan statistic, Poisson process, higher dimensions, unconditional, simulation.

1999-09-16, Sven Erick Alm,