A new estimation method for Weibull-type tails based on the mean excess function

Abstract

Studying the right tail of a distribution, one can classify the distributions into three classes based on the extreme value index γ . The class γ > 0 corresponds to Pareto-type or heavy tailed distributions, while γ < 0 indicates that the underlying distribution has a finite endpoint. The Weibull-type distributions form an important subgroup within the Gumbel class with γ = 0 . The tail behaviour can then be specified using the Weibull tail index. Classical estimators of this index show severe bias. In this paper we present a new estimation approach based on the mean excess function, which exhibits improved bias and mean squared error. The asserted properties are supported by simulation experiments and asymptotic results. Illustrations with real life data sets are provided.