Functional peaks?over?threshold analysis

Abstract Peaks-over-threshold analysis using the generalised Pareto distribution is widely applied in modelling tails of univariate random variables, but much information may be lost when complex extreme events are studied results. In this paper, we extend peaks-over-threshold to extremes functional data. Threshold exceedances defined a r modelled by r-Pareto process, generalisation that covers three classical regimes for decay tail probabilities, and only possible continuous limit r-exceedances properly rescaled process. We give construction rules, simulation algorithms inference procedures processes, discuss model validation apply new methodology European windstorms heavy spatial rainfall.