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Skew generalized extreme value distribution: Probability-weighted moments estimation and application to block maxima procedure
Authors:Pierre Ribereau  Esterina Masiello  Philippe Naveau
Institution:1. Université de Lyon, Université Lyon 1, CNRS, Institut Camille Jordan, Villeurbanne-Cedex, Francepierre.ribereau@univ-lyon1.fr;3. Université de Lyon, Université Lyon 1, CNRS, Institut Camille Jordan, Villeurbanne-Cedex, France;4. Laboratoire des Sciences du Climat et de l’Environnement, IPSL-CNRS, Gif-sur-Yvette, France
Abstract:ABSTRACT

Following the work of Azzalini (1985 Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Stat. 12:171178.Web of Science ®] Google Scholar] and 1986 Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones. Statistica 46:199208. Google Scholar]) on the skew-normal distribution, we propose an extension of the generalized extreme value (GEV) distribution, the SGEV. This new distribution allows for a better fit of maxima and can be interpreted as both the distribution of maxima when maxima are taken on dependent data and when maxima are taken over a random block size. We propose to estimate the parameters of the SGEV distribution via the probability-weighted moment method. A simulation study is presented to provide an application of the SGEV on block maxima procedure and return level estimation. The proposed method is also implemented on a real-life data.
Keywords:Extreme value theory  Generalized extreme value distribution  Probability-weighted moments  Return level estimation  Skew distributions
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