Threshold detection for the generalized Pareto distribution: Review of representative methods and application to the NOAA NCDC daily rainfall database

Abstract

In extreme excess modeling, one fits a generalized Pareto (GP) distribution to rainfall excesses above a properly selected threshold u. The latter is generally determined using various approaches, such as nonparametric methods that are intended to locate the changing point between extreme and nonextreme regions of the data, graphical methods where one studies the dependence of GP-related metrics on the threshold level u, and Goodness-of-Fit (GoF) metrics that, for a certain level of significance, locate the lowest threshold u that a GP distribution model is applicable. Here we review representative methods for GP threshold detection, discuss fundamental differences in their theoretical bases, and apply them to 1714 overcentennial daily rainfall records from the NOAA-NCDC database. We find that nonparametric methods are generally not reliable, while methods that are based on GP asymptotic properties lead to unrealistically high threshold and shape parameter estimates. The latter is justified by theoretical arguments, and it is especially the case in rainfall applications, where the shape parameter of the GP distribution is low; i.e., on the order of 0.1-0.2. Better performance is demonstrated by graphical methods and GoF metrics that rely on preasymptotic properties of the GP distribution. For daily rainfall, we find that GP threshold estimates range between 2 and 12 mm/d with a mean value of 6.5 mm/d, while the existence of quantization in the empirical records, as well as variations in their size, constitute the two most important factors that may significantly affect the accuracy of the obtained results.