Parameter and quantile estimation for the generalized Pareto distribution in peaks over threshold framework

In this article, we consider six estimation methods for extreme value modeling and compare their performances, focusing on the generalized Pareto distribution (GPD) in the peaks over threshold (POT) framework. Our goal is to identify the best method in various conditions via a thorough simulation study. In order to compare the estimators in the POT sense, we suggest proper strategies for some estimators originally not developed under the POT framework. The simulation results show that a nonlinear least squares (NLS) based estimator outperforms others in parameter estimation, but there is no clear winner in quantile estimation. For quantile estimation, NLS-based methods perform well even when the sample size is small and the Hill estimator comes to the front when the underlying distribution has a very heavy tail. Applications of EVT cover many different fields and researchers on each field may have their own experimental conditions or practical restrictions. We believe that our results would provide guidance on determining proper estimation method on future analysis.