A note on the Poisson assumption in partial duration series models

Abstract

The Poisson process is frequently encountered in probability models of the partial duration series. This paper looks at the necessity for specifying the model in detail by such a process and also examines the validity of the Poisson distribution, in this context, as judged on data from 26 gaging stations on 20 catchments in Great Britain. When all the data are considered jointly the Poisson assumption has to be rejected although it is acceptable in some cases. It is also suggested that if dependence exists in the partial duration series it should be looked for in the point process from which the series arises rather than among successive peak magnitudes.