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Simulation and prediction of extremes

Martin Schlather, School of Business Informatics and Mathematics, Universität Mannheim

Here, we deal with two aspects of extreme value statistics for predicting weather extremes: the efficient simulation of max-stable random fields and the ECC approach for extremes. The ECC approach for postprocessing based on the empirical copula discussed in Section 3.2 above is an appealing approach whenever the values are in within the bulk of the distribution. It is well-known that the extreme values of a distribution may behave quite differently from those in the bulk and often, too few values in the tail are available for reliable non-parametric inference. Brown-Resnick processes and their multivariate marginal Hüsler-Reiss distributions allow for flexible, parametric models for extreme values. Furthermore, specific estimation methods and simulation techniques that have been made available during the first WEX-MOP phase can be utilized here.

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