Revisiting some estimation methods for the generalized Pareto distribution

SummaryThe generalized Pareto distribution (GPD) is widely used in hydrological frequency analysis, especially in the peaks-over-threshold (POT) modeling of hydrological extremes. The methods of maximum likelihood (ML), of moments (MM), of probability weighted moments (PWM), and of generalized probability weighted moments (GPWM), are some of the principal methods proposed for fitting the GPD model. When its shape parameter is positive, the GPD has a finite upper bound that is a function of the distribution parameters. It has been largely overlooked in the hydrological literature that certain fitting methods may produce estimates of this upper bound that are inconsistent with the observed data. This inconsistency occurs when one or more sample observations exceed the estimated upper bound. This article sheds more light on this problem of inconsistency with the data, and assesses its consequences through Monte Carlo simulations. New guidelines are provided for choosing between the ML, MM, PWM and GPWM methods for estimating GPD quantiles.