Estimation of extreme quantiles from heavy and light tailed distributions |
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Authors: | Jonathan El Methni Laurent Gardes Stéphane Girard Armelle Guillou |
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Institution: | 1. Team Mistis, INRIA Rhône-Alpes & LJK, Inovallée, 655, av. de l''Europe, Montbonnot, 38334 Saint-Ismier cedex, France;2. Université de Strasbourg & CNRS, IRMA, UMR 7501, 7 rue René Descartes, 67084 Strasbourg cedex, France |
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Abstract: | In Gardes et al. (2011), a new family of distributions is introduced, depending on two parameters τ and θ, which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for θ and extreme quantiles are also proposed, but they both depend on the unknown parameter τ, making them useless in practical situations. In this paper, we propose an estimator of τ which is independent of θ. Plugging our estimator of τ in the two previous ones allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unified way. The asymptotic distributions of our three new estimators are established and their efficiency is illustrated on a small simulation study and on a real data set. |
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Keywords: | Weibull tail-distributions Pareto-type distributions Extreme quantile Maximum domain of attraction Asymptotic normality |
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