2010
DOI: 10.1029/2009wr009040
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Multivariate multiparameter extreme value models and return periods: A copula approach

Abstract: [1] Multivariate extreme value models are a fundamental tool in order to assess potentially dangerous events. The target of this paper is two-fold. On the one hand we outline how, exploiting recent theoretical developments in the theory of copulas, new multivariate extreme value distributions can be easily constructed; in particular, we show how a suitable number of parameters can be introduced, a feature not shared by traditional extreme value models. On the other hand, we introduce a proper new definition of… Show more

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Cited by 249 publications
(150 citation statements)
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“…Only very limited applications can be found in the literature with multivariate analysis of rainfall (Gräler 2014;Gyasi-Agyei and Melching 2012;Zhang and Singh 2007;Kao and Govindaraju 2008;Salvadori and De Michele 2006;Grimaldi and Serinaldi 2006), floods (Zhang and Singh 2014;Xiong et al 2014;Chen et al 2012;Serinaldi and Grimaldi 2007;Genest et al 2007;Salvadori and De Michele 2010) and droughts (Kao and Govindaraju 2010;Song and Singh 2010;Wong et al 2010).…”
Section: Copulasmentioning
confidence: 99%
“…Only very limited applications can be found in the literature with multivariate analysis of rainfall (Gräler 2014;Gyasi-Agyei and Melching 2012;Zhang and Singh 2007;Kao and Govindaraju 2008;Salvadori and De Michele 2006;Grimaldi and Serinaldi 2006), floods (Zhang and Singh 2014;Xiong et al 2014;Chen et al 2012;Serinaldi and Grimaldi 2007;Genest et al 2007;Salvadori and De Michele 2010) and droughts (Kao and Govindaraju 2010;Song and Singh 2010;Wong et al 2010).…”
Section: Copulasmentioning
confidence: 99%
“…Clearly, other models could be more indicated for describing the random behavior of data sets different from the one investigated here. An algorithm for simulatingĈ is outlined in Durante and Salvadori [2010] and Salvadori and De Michele [2010].…”
Section: Multivariate Frequency Analysismentioning
confidence: 99%
“…[25] Similarly, considering the duration D, the Weibull distribution is always selected as the best AIC model, over all the N R randomizations (see Figure 2 The ''Clayton,'' ''Gumbel,'' and ''Frank'' labels denote the corresponding families of Archimedean 2-copulas [Nelsen, 2006;Salvadori et al, 2007]; the labels ''Mix[AB]'' denote a convex mixture C of the two families A and B indicated (i.e., C ¼ A þ 1 À ð ÞB with 2 0; 1 ½ ); the labels ''X[AB]'' denote the Khoudraji-Liebscher extraparametrization C of the two families A and B indicated [Durante and Salvadori, 2010;Salvadori and De Michele, 2010].…”
Section: Univariate Frequency Analysismentioning
confidence: 99%
See 1 more Smart Citation
“…As prescribed in Genest and Favre [2007], several bivariate copula families (like e.g., the Clayton, Frank, Gumbel, Gaussian, t-Student, their convex mixtures, and the corresponding extraparameterized Khoudraji-Liebscher's versions [Durante and Salvadori, 2010;Salvadori and De Michele, 2010]) are fitted on the (normalized) survival ranks of the data. As a result, the following three-parameter convex mixtureĈ of the Clayton (A) and the Gumbel (B) copulas turns out to be appropriate according to both the (corrected) Akaike and the Bayesian information criteria :Ĉ u; ; ; ð Þ¼ A u; ð Þþ 1 À ð ÞB u; ð Þ, where the ranges of the parameters are !…”
Section: Case Studymentioning
confidence: 99%