Estimation of the Weibull tail-coefficient with linear combination of upper order statistics

Laurent Gardes (1) , Stéphane Girard (1)

1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems

We present a new family of estimators of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse failure rate function. Our estimators are based on a linear combination of log-spacings of the upper order statistics. Their asymptotic normality is established and illustrated for two particular cases of estimators in this family. Their finite sample performances are presented on a simulation study.

Mots clés: Weibull tail-coefficient; Extreme-values; Order statistics; Regular variations

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Laurent Gardes, Stéphane Girard. Estimation of the Weibull tail-coefficient with linear combination of upper order statistics. Journal of Statistical Planning and Inference, 2008, 138 (5), pp.1416-1427. ⟨10.1016/j.jspi.2007.04.026⟩. ⟨hal-00821187⟩