A weighted mean excess function approach to the estimation of Weibull-type tails

A new class of estimators for the Weibull-tail coefficient is proposed. The estimators are based on linear combinations of log-spacings of the mean excess function evaluated at high levels. The asymptotic distribution of this new class of estimators is derived under some mild conditions on the weight function and a second order condition on the tail behavior. The finite sample properties of some estimators obtained with important special cases of the weight function are examined with a small simulation experiment.