1. Estimation of extreme quantiles from heavy and light tailed distributions
- Author
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Armelle Guillou, Stéphane Girard, Laurent Gardes, Jonathan El Methni, Modelling and Inference of Complex and Structured Stochastic Systems (MISTIS), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique Avancée (IRMA), and Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Statistics and Probability ,Asymptotic distribution ,01 natural sciences ,010104 statistics & probability ,Weibull tail-distributions ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,0502 economics and business ,Statistics ,Pareto-type distributions ,Asymptotic normality ,0101 mathematics ,Maximum domain of attraction ,Exponentiated Weibull distribution ,050205 econometrics ,Mathematics ,Weibull distribution ,Estimation ,Extreme quantile ,Applied Mathematics ,05 social sciences ,Estimator ,[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ,Trimmed estimator ,Data set ,Statistics, Probability and Uncertainty ,Quantile - Abstract
International audience; In Gardes et al. (2011), a new family of distributions is introduced, depending on two parameters tau and theta which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for theta and extreme quantiles are also proposed, but they both depend on the unknown parameter tau, making them useless in practical situations. In this paper, we propose an estimator of tau which is independent of theta. Plugging our estimator of tau in the two previous ones allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unifi ed 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.
- Published
- 2012
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