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

## Sven Erick Alm

### 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