Copula Modeling for Extremes

Abstract

This article introduces extreme‐value copulas, reviews models from this class, and describes their main properties. The associated rank‐based estimation procedures and model validation techniques are also presented.

When Gumbel met Galambos

“…in terms of a function : [12,15,19] whose analytical characterization is given in [3,34]. The stable tail dependence function of the Gumbel copula with parameter ρ ∈ (0, 1) is given, for all…”

Generalized Pareto copulas: A key to multivariate extremes

“…, log(u d )) D ) , u ∈ (0, 1] d , with some D-norm · D . For a discussion of parametric families of extreme value copulas and their statistical analysis we refer to Genest and Nešlehová (2012).…”

Integrating Entropy and Copula Theories for Hydrologic Modeling and Analysis

“…Copulas have been commonly used in hydrology for the dependence modeling in a variety of applications, including frequency analysis [1,2,68,69], streamflow or rainfall simulation [22,70], geo-statistical interpolation [70], bias correction [71], uncertainty analysis [72], downscaling [73], and statistical forecasting [74]. Several review papers are available for the theory and application of copulas in hydrology [7,[12][13][14][75][76][77].…”

“…Entropy is a measure of uncertainty of random variables and has been used for a variety of applications in hydrology [6,[8][9][10]. Copulas provide a flexible way to construct joint distributions of random variables, independent of their marginal probability distributions, and have spurred a flurry of applications in hydrology in recent years [7,[11][12][13][14][15]. The entropy and copula theories have mostly been developed in relative isolation in the past decades.…”