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Journal Articles REVSTAT - Statistical Journal Year : 2024

A refined extreme quantiles estimator for Weibull tail-distributions

Abstract

We address the estimation of extreme quantiles of Weibull tail-distributions. Since such quantiles are asymptotically larger than the sample maximum, their estimation requires extrapolation methods. In the case of Weibull tail-distributions, classical extreme-value estimators are numerically outperformed by estimators dedicated to this set of light-tailed distributions. The latter estimators of extreme quantiles are based on two key quantities: an order statistic to estimate an intermediate quantile and an estimator of the Weibull tail-coefficient used to extrapolate. The common practice is to select the same intermediate sequence for both estimators. We show how an adapted choice of two different intermediate sequences leads to a reduction of the asymptotic bias associated with the resulting refined estimator. This analysis is supported by an asymptotic normality result associated with the refined estimator. A data-driven method is introduced for the practical selection of the intermediate sequences and our approach is compared to three estimators of extreme quantiles dedicated to Weibull tail-distributions on simulated data. An illustration on a real data set of daily wind measures is also provided.
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Dates and versions

hal-04022982 , version 1 (10-03-2023)
hal-04022982 , version 2 (14-06-2023)
hal-04022982 , version 3 (10-01-2024)

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  • HAL Id : hal-04022982 , version 3

Cite

Jonathan El Methni, Stéphane Girard. A refined extreme quantiles estimator for Weibull tail-distributions. REVSTAT - Statistical Journal, In press. ⟨hal-04022982v3⟩
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