Estimating an endpoint with high order moments in the Weibull domain of attraction

Stephane Girard; Armelle Guillou; Gilles Stupfler

doi:10.1016/j.spl.2012.07.005

Estimating an endpoint with high order moments in the Weibull domain of attraction

Stephane Girard ¹ Armelle Guillou ² Gilles Stupfler ³

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

2 IRMA - Institut de Recherche Mathématique Avancée

3 CERGAM - Centre d'Études et de Recherche en Gestion d'Aix-Marseille

Abstract : We present a method for estimating the endpoint of a unidimensional sample when the distribution function belongs to the Weibull-max domain of attraction. The approach relies on transforming the variable of interest and then using high order moments of the positive variable obtained this way. It is assumed that the order of the moments goes to infinity. We give conditions on the rate of divergence to get the weak and strong consistency as well as the asymptotic normality of the estimator. The good performance of the estimator is illustrated on some finite sample situations.

Keywords : Endpoint estimation high order moments consistency asymptotic normality

Document type :

Journal articles

Domain :

Mathematics [math] / Statistics [math.ST]

Statistics [stat] / Statistics Theory [stat.TH]

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https://hal.archives-ouvertes.fr/hal-00648435
Contributor : Gilles Stupfler <>
Submitted on : Friday, November 30, 2012 - 4:12:02 PM
Last modification on : Friday, May 4, 2018 - 1:02:12 AM
Document(s) archivé(s) le : Friday, March 1, 2013 - 3:56:55 AM

weibull_logratio_revised.pdf

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