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

1985/08/01 by J. R. M. Hosking, J. R. Wallis, James R. Wallis +2 · 7 citations
Mathematics · Decision Sciences · Economics, Econometrics and Finance · #Statistical Distribution Estimation and Applications #Probabilistic and Robust Engineering Design #Financial Risk and Volatility Modeling

paper · doi:10.1080/00401706.1985.10488049

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.

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