# On the distributions of the scan statistics of a Poisson process

#### by

## Sven Erick Alm

#### Uppsala University

##### in Probability and Mathematical Statistics, Essays in honour of
Carl-Gustav Esseen. Uppsala, Sweden, 1983

### Abstract

Let *X* be a Poisson process with intensity $\lambda$ and let
*Y (Y(t)=X(t)-X(t-a))* be the associated scanning process.

The distribution of the scan statistic, *N* (max *Y* over the
interval (0,*T*)) is approximated.

The approximation is numerically simple, and, for small values of
*a/T*, very accurate.

1995-02-06, Sven Erick Alm, sea@math.uu.se