Brief Communication: Statistical detection and modeling of the over-dispersion of winter storm occurrence

In this communication, I discuss and improve the detection and modeling of the over-dispersion of winter storm occurrence using the example of Germany. For this purpose, the generalized Poisson distribution and information criterions for the model selection are introduced. Correct statistical model selection ensures the statistical significance of the model, including a possible over-dispersion. Moreover, I derive the relation between expectation and variance of a thinned inhomogeneous Poisson process. This is also applied to well detect the over-dispersion in winter storm data for Germany of Karremann et al. (2014).