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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 15, issue 6
Nonlin. Processes Geophys., 15, 1033–1039, 2008
https://doi.org/10.5194/npg-15-1033-2008
© Author(s) 2008. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 15, 1033–1039, 2008
https://doi.org/10.5194/npg-15-1033-2008
© Author(s) 2008. This work is distributed under
the Creative Commons Attribution 3.0 License.

  23 Dec 2008

23 Dec 2008

Estimating return levels from maxima of non-stationary random sequences using the Generalized PWM method

P. Ribereau1, A. Guillou2, and P. Naveau3 P. Ribereau et al.
  • 1Université Montpellier 2, Equipe Proba-Stat, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
  • 2Université de Strasbourg, IRMA; 7, rue René Descartes, 67084 Strasbourg Cedex, France
  • 3Laboratoire des Sciences du Climat et de l'Environnement, IPSL-CNRS, Orme des Merisiers, 91191 Gif-sur-Yvette, France

Abstract. Since the pioneering work of Landwehr et al. (1979), Hosking et al. (1985) and their collaborators, the Probability Weighted Moments (PWM) method has been very popular, simple and efficient to estimate the parameters of the Generalized Extreme Value (GEV) distribution when modeling the distribution of maxima (e.g., annual maxima of precipitations) in the Identically and Independently Distributed (IID) context. When the IID assumption is not satisfied, a flexible alternative, the Maximum Likelihood Estimation (MLE) approach offers an elegant way to handle non-stationarities by letting the GEV parameters to be time dependent. Despite its qualities, the MLE applied to the GEV distribution does not always provide accurate return level estimates, especially for small sample sizes or heavy tails. These drawbacks are particularly true in some non-stationary situations. To reduce these negative effects, we propose to extend the PWM method to a more general framework that enables us to model temporal covariates and provide accurate GEV-based return levels. Theoretical properties of our estimators are discussed. Small and moderate sample sizes simulations in a non-stationary context are analyzed and two brief applications to annual maxima of CO2 and seasonal maxima of cumulated daily precipitations are presented.

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