Publications related to Extreme value theory

Functional peaks-over-threshold analysis

Anthony Christopher Davison, Raphaël Gérard Théodore Michel Marie de Deloÿe et Fourcade de Fondeville

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 using univariate results. In this paper, w ...

WILEY2022

Causal modelling of heavy-tailed variables and confounders with application to river flow

Anthony Christopher Davison, Valérie Chavez

Confounding variables are a recurrent challenge for causal discovery and inference. In many situations, complex causal mechanisms only manifest themselves in extreme events, or take simpler forms in the extremes. Stimulated by data on extreme river flows a ...

SPRINGER2022

Sub‐asymptotic motivation for new conditional multivariate extreme models

Anthony Christopher Davison, Thomas Lugrin, Jonathan A. Tawn

Statistical models for extreme values are generally derived from non-degenerate probabilistic limits that can be used to approximate the distribution of events that exceed a selected high threshold. If convergence to the limit distribution is slow, then th ...

2021

Multivariate extremes over a random number of observations

Simone Padoan, Stefano Rizzelli

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated data, such as max ...

WILEY2021

Inference on the Angular Distribution of Extremes

Claudio Andri Semadeni

The spectral distribution plays a key role in the statistical modelling of multivariate extremes, as it defines the dependence structure of multivariate extreme-value distributions and characterizes the limiting distribution of the relative sizes of the co ...

EPFL2020

Extremal behaviour of aggregated data with an application to downscaling

Sebastian Engelke, Raphaël Gérard Théodore Michel Marie de Deloÿe et Fourcade de Fondeville

The distribution of spatially aggregated data from a stochastic process may exhibit tail behaviour different from that of its marginal distributions. For a large class of aggregating functionals we introduce the -extremal coefficient, which quantifies this ...

OXFORD UNIV PRESS2019

Functional Peaks-Over-Threshold Analysis for Complex Extreme Events

Most current risk assessment for complex extreme events relies on catalogues of similar events, either historical or generated artificially. In the latter, no existing methods produce completely new events with mathematically justified extrapolation above ...

EPFL2018

Contributions to Modelling Extremes of Spatial Data

Linda Frossard

The increasing interest in using statistical extreme value theory to analyse environmental data is mainly driven by the large impact extreme events can have. A difficulty with spatial data is that most existing inference methods for asymptotically justifie ...

EPFL2017

Likelihood estimators for multivariate extremes

Anthony Christopher Davison, Raphaël Huser

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of componentwise maxima, high t ...

Springer2016

Monitoring-based safety verification at the Ultimate Limit State of fracture of the RC slab of a short span railway underpass

Eugen Brühwiler, Vasileios Grigoriou

The examination value of the railway traffic action effect is calculated from long-term monitoring data without resorting to load models and structural analysis. Monitoring data are obtained from measurements on a short span RC slab bridge. The action effe ...

Elsevier Science Bv2016

Sample and population exponents of generalized Taylor's law

Andrea Rinaldo, Andrea Giometto, Amos Maritan

Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. It ...

National Academy of Sciences2015

Dual sourcing under heavy-tailed demand: an extreme value theory approach

Isik Bicer

We consider a single-period dual-sourcing problem in which a buyer purchases its products from two different suppliers and sells them to a market with uncertain demand. One supplier is cheaper but less responsive, whereas the other supplier is more respons ...

Taylor & Francis Ltd2015

Geostatistics of Dependent and Asymptotically Independent Extremes

Anthony Christopher Davison, Emeric Rolland Georges Thibaud, Raphaël Huser

Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infras ...

Springer Heidelberg2013

A new representation for multivariate tail probabilities

Jennifer Lynne Wadsworth, Jonathan A. Tawn

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the effect of allowing t ...

Bernoulli Society for Mathematical Statistics and Probability2013

A Euclidean Likelihood Estimator for Bivariate Tail Dependence

Michal Warchol, Boris Oumow

The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the ...

Taylor & Francis Inc2013

On the relationship between total ozone and atmospheric dynamics and chemistry at mid-latitudes - Part 1: Statistical models and spatial fingerprints of atmospheric dynamics and chemistry

Anthony Christopher Davison, Linda Frossard

We use statistical models for mean and extreme values of total column ozone to analyze "fingerprints" of atmospheric dynamics and chemistry on long-term ozone changes at northern and southern mid-latitudes on grid cell basis. At each grid cell, the r-large ...

Copernicus Publications2013

Extreme rainfall in West Africa: A regional modeling

Juliette Ferial Blanchet, Adnan Ali

In a world of increasing exposure of populations to natural hazards, the mapping of extreme rainfall remains a key subject of study. Such maps are required for both flood risk management and civil engineering structure design, the challenge being to take i ...

Amer Geophysical Union2012

Extreme events in total ozone over the Northern mid-latitudes: an analysis based on long-term data sets from five European ground-based stations

Anthony Christopher Davison

We apply methods from extreme value theory to identify extreme events in high (termed EHOs) and low (termed ELOs) total ozone and to describe the distribution tails (i.e. very high and very low values) of five long-term European ground-based total ozone ti ...

2011

Extreme events in total ozone over Arosa---Part 1: Application of extreme value theory

Anthony Christopher Davison

In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean v ...

Copernicus Publications2010

Normalization of network generalized extreme value models

Jeffrey Newman

Generalized extreme value (GEV) models provide a convenient way to model choice behavior that is consistent with utility maximization theory, but the development of specific new models within the GEV family has been slow, due to the difficulty of ensuring ...

2008