On the distributions of the scan statistics of a Poisson process
Sven Erick Alm
in Probability and Mathematical Statistics, Essays in honour of
Carl-Gustav Esseen. Uppsala, Sweden, 1983
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.