Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 15 6 2008 10.5194/npg-15-1033-2008 http://www.nonlin-processes-geophys.net/15/1033/2008/ http://www.nonlin-processes-geophys.net/15/1033/2008/npg-15-1033-2008.html http://www.nonlin-processes-geophys.net/15/1033/2008/npg-15-1033-2008.pdf 1033 1039 2008-12-23 Estimating return levels from maxima of non-stationary random sequences using the Generalized PWM method P. Ribereau pribere@math.univ-montp2.fr A. Guillou P. Naveau Université Montpellier 2, Equipe Proba-Stat, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France Université de Strasbourg, IRMA; 7, rue René Descartes, 67084 Strasbourg Cedex, France Laboratoire des Sciences du Climat et de l'Environnement, IPSL-CNRS, Orme des Merisiers, 91191 Gif-sur-Yvette, France 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. 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