Estimation of the Generalized Extreme-Value Distribution by the Method of Probability-Weighted Moments

Abstract

We use the method of probability-weighted moments to derive estimators of the parameters and quantiles of the generalized extreme-value distribution. We investigate the properties of these estimators in large samples, via asymptotic theory, and in small and moderate samples, via computer simulation. Probability-weighted moment estimators have low variance and no severe bias, and they compare favorably with estimators obtained by the methods of maximum likelihood or sextiles. The method of probability-weighted moments also yields a convenient and powerful test of whether an extreme-value distribution is of Fisher-Tippett Type I, II, or III.