Statistical models for over-dispersion in the frequency of peaks over threshold data for a flow series.

In a peaks over threshold analysis of a series of river flows, a sufficiently high threshold is used to extract the peaks of independent flood events. This paper reviews existing, and proposes new, statistical models for both the annual counts of such events and the process of event peak times. The most common existing model for the process of event times is a homogeneous Poisson process. This model is motivated by asymptotic theory. However, empirical evidence suggests that it is not the most appropriate model, since it implies that the mean and variance of the annual counts are the same, whereas the counts appear to be overdispersed, i.e., have a larger variance than mean. This paper describes how the homogeneous Poisson process can be extended to incorporate time variation in the rate at which events occur and so help to account for overdispersion in annual counts through the use of regression and mixed models. The implications of these new models on the implied probability distribution of the annual maxima are also discussed. The models are illustrated using a historical flow series from the River Thames at Kingston.