The Peaks-Over-Threshold Method

A common approach to practical extreme value analysis is to use the GEV form of the asymptotic extreme value distributions to fit to the observed extreme values. The typical data that are used in this process are the extreme values observed over specified periods of time, e.g., over 1 year periods. Such a procedure, extracting only extremes over blocks of data, would immediately appear to be wasteful, since potentially very useful data might be discarded. The Peaks-Over-Threshold method, or simply the POT method, represents an approach to extreme value analysis that tries to avoid this waste of data by considering all data that exceed a prescribed high threshold. It will be shown that also for the POT method there are three limiting forms of the exceedance probability distributions corresponding to the Extremal Types Theorem. The Generalized Pareto (GP) distribution will take the place of the GEV distribution.