Examination for robustness of parametric estimators for flood statistics in the context of extraordinary extreme events

Abstract

We compare several estimators, which are commonly used in hydrology, for the parameters of the distribution of flood series, like the Maximum-Likelihood estimator or L-Moments, with the robust estimators Trimmed L-Moments and Minimum Distances. Our objective is estimation of the 99 %- or 99.9 %-quantile of an underlying Gumbel or Generalized Extreme Value distribution (GEV), where we modify the generated random variables such that extraordinary extreme events occur. The results for a two- or three-parametric fitting are compared and the robustness of the estimators to the occurrence of extraordinary extreme events is investigated by statistical measures. When extraordinary extreme events are known to appear in the sample, the Trimmed L-Moments are a recommendable choice for a robust estimation. They even perform rather well, if there are no such events.