Mathematics – Probability
Scientific paper
2012-03-12
Mathematics
Probability
19 pages, 2 figures
Scientific paper
In extreme value statistics the peaks-over-threshold method is widely used. The method is based on the Generalized Pareto distribution (Balkema and de Haan (1974), Pickands (1975) in univariate theory and e.g. Falk, H\"usler and Reiss (2010), Rootz\'en and Tajvidi (2006) in multivariate theory) characterizing probabilities of exceedances over high thresholds. We present a generalization of this concept in the space of continuous functions. We call this the Generalized Pareto process. Different from earlier papers our definition is not based on a distribution function but on functional properties. As an application we use the theory to produce wind fields connected to disastrous storms on the basis of observed extreme but not disastrous storms.
Ferreira Ana
Haan Laurens de
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