A semi‐parametric stochastic generator for bivariate extreme events

Abstract

The analysis of multiple extreme values aims to describe the stochastic behaviour of observations in the joint upper tail of a distribution function. For instance, being able to simulate multivariate extreme events is convenient for end users who need a large number of random replications of extremes as input of a given complex system to test its sensitivity. The simulation of multivariate extremes is often based on the assumption that the dependence structure, the so-called extremal dependence function, is described by a specific parametric model. We propose a simulation method for sampling bivariate extremes, under the assumption that the extremal dependence function is semiparametric. This yields a flexible tool that can be broadly applied in real-data analyses. With the aim of estimating the probability of belonging to some extreme sets, our methodology is examined via simulation and illustrated by an analysis of strong wind gusts in France.Stat 2017; 6: 184-201 6 Analysis of high wind gustsDesigning infrastructures often requires the study of strong WGs. We illustrate the utility of our methodology analysing this type of natural process. We consider the hourly WG in metres per second, hourly WS in metres per second (m/s) and hourly air pressure at sea level in millibars recorded in Parcay-Meslay city in the northwest of France, from July 2004 to July 2013 (upper panels of Figure 4). We focus on WG and WS when a positive increment for the daily range of the air pressure (IP) is observed. Note that often strong wind takes place with stormy weather, and this implies a

Estimation and uncertainty quantification for extreme quantile regions

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New estimation methods for extremal bivariate return curves

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Estimation of the multivariate conditional tail expectation for extreme risk levels: Illustration on environmental data sets

“…In this second application, we focus on the study of strong WGs. These data come from a larger data set previously analyzed by Marcon, Naveau, and Padoan (). We consider 2 weeks maximum wind speed (WS) in meters per second, WG in meters per second, and positive increment air pressure (IP) at the sea level in millibar recorded in Parçay‐Meslay city in the northwest of France, from July 2004 to July 2013 (see Figure , left).…”