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A note of caution when interpreting parameters of the distribution of excesses
Authors:Pierre Ribereau  Philippe NaveauArmelle Guillou
Institution:a Université de Montpellier II, I3M, CC051, Place Eugéne Bataillon, 34090 Montpellier, France
b CNRS, IPSL, Laboratoire des Sciences du Climat et de l’Environnement, Orme des Merisiers/Bat. 701, C.E. Saclay, 91191 Gif-sur-Yvette, France
c Université de Strabourg, CNRS, IRMA UMR 7501, 7 rue André Descartes, 67084 Strabourg Cedex, France
Abstract:In climatology and hydrology, univariate Extreme Value Theory has become a powerful tool to model the distribution of extreme events. The Generalized Pareto Distribution (GPD) is routinely applied to model excesses in space or time by letting the two GPD parameters depend on appropriate covariates. Two possible pitfalls of this strategy are the modeling and the interpretation of the scale and shape GPD parameters estimates which are often and incorrectly viewed as independent variables. In this note we first recall a statistical technique that makes the GPD estimates less correlated within a Maximum Likelihood (ML) estimation approach. In a second step we propose novel reparametrizations for two method-of-moments particularly popular in hydrology: the Probability Weighted Moment (PWM) method and its generalized version (GPWM). Finally these three inference methods (ML, PWM and GPWM) are compared and discussed with respect to the issue of correlations.
Keywords:Generalized Pareto Distribution  Reparametrization  Probability Weighted Moment  Maximum Likelihood  Extreme Value Theory  Generalized Extreme Value Distribution
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