Comparison between classical annual maxima and peak over threshold approach concerning robustness

Abstract

Partial duration series (peak over threshold) form a considerable alternative to the classical annual maximum approach since they enlarge the information spectrum. The classical POT approach is based on a Poisson distribution for the annual number of exceedances although this is can be questionable in some cases. Therefore two different distributions (Binomial and Gumbel-Schelling (Gumbel and Schelling (1950)) ) are considered. The results show that they do rarely make a difference to the Poisson distribution. In a second step we investigate the robustness in the sense of stability against the occurrence of extreme events of the POT compared to annual maxima and show that in the case of extreme events the POT behaves much more robust and fits very good to the data.