Parameter estimation for the general extreme value distribution

This study is concerned with the estimation of the parameters of the general (or generalised) extreme value (GEV) distribution by the methods of maximum likelihood (ML) and probability-weighted moments (PWM) for complete and type I censored samples. For complete samples, the PWM provided estimators which are less biased than the ML estimators. For the variances/covariances of the parameter estimators, the PWM had a comparable efficiency to the ML. However, for the extreme quantiles, the PWM estimators had much larger variances. For censored samples, the extension provided in this study for the PWM did not perform satisfactorily in terms of the bias and variances of the estimators. The ML, on the other hand, still functioned well. It can reduce the bias and even the variances of the estimators at some censoring levels. Finally, the Akaike information criterion, used along with the ML estimators, can identify the extremal models with a high accuracy level for both complete and censored samples.