Improving Probability-Weighted Moment Methods for the Generalized Extreme Value Distribution

Abstract

In 1985 Hosking et al. estimated with the so-called Probability-Weighted Moments (PWM) method the parameters of the Generalized Extreme Value (GEV) distribution, the latter being classically fitted to maxima of sequences of independent and identically distributed random variables. Their approach is still very popular in hydrology and climatology because of its conceptual simplicity, its easy implementation and its good performance for most distributions encountered in geosciences. Its main drawback resides in its limitations when applied to strong heavy-tailed densities. Whenever the GEV shape parameter is larger than 0.5, the asymptotic properties of the PWMs cannot be derived and consequently, asymptotic confidence intervals cannot be obtained. To broaden the validity domain of the PWM approach, we take advantage of a recent extension of PWM to a larger class of moments, called Generalized PWM (GPWM). This allows us to derive the asymptotic properties of our estimators for larger values of the shape parameter. The performance of our approach is illustrated by studying simulations of small, medium and large GEV samples. Comparisons with other GEV estimation techniques used in hydrology and climatology are performed.