Weibull tail-distributions revisited: a new look at some tail estimators

Laurent Gardes 1 Stephane Girard 1 Armelle Guillou 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In this paper, we propose to include Weibull tail-distributions in a more general family of distributions. In particular, the considered model also encompasses the whole Fréchet maximum domain of attraction as well as log-Weibull tail-distributions. The asymptotic normality of some tail estimators based on the log-spacings between the largest order statistics is established in an unified way within the considered family. This result permits to understand the similarity between most estimators of the Weibull tail-coefficient and the Hill estimator. Some different asymptotic properties, in terms of bias, rate of convergence, are also highlighted.
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Journal of Statistical Planning and Inference, Elsevier, 2011, 141 (1), pp.429-444. 〈10.1016/j.jspi.2010.06.018〉
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Laurent Gardes, Stephane Girard, Armelle Guillou. Weibull tail-distributions revisited: a new look at some tail estimators. Journal of Statistical Planning and Inference, Elsevier, 2011, 141 (1), pp.429-444. 〈10.1016/j.jspi.2010.06.018〉. 〈hal-00340661v4〉

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