Journal of Statistical Planning and Inference vol:139 issue:6 pages:1905-1920
Studying the right tail of a distribution, one can classify the distributions into three classes based on the extreme value index gamma. The class gamma > 0 corresponds to Pareto-type or heavy tailed distributions, while gamma < 0 indicates that the underlying distribution has a finite endpoint. The Weibull-type distributions form an important subgroup within the Gumbel class with gamma = 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. (c) 2008 Elsevier B.V. All rights reserved.