Extremes in Nature : an approach using Copulas

By G. Salvadori, Carlo De Michele, N. T. Kottegoda, Renzo Rosso. 2007

584 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f6e1e32428d94cf8dff9316e919db72c8b8dbe06

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Citations in the corpus

Multivariate multiparameter extreme value models and return periods: A copula approach (2010, methodology): “Most importantly, by exploiting the invariance property of copulas [Nelsen, 2006; Salvadori et al., 2007], we may restrict our attention to copulas only, and do not worry about the GEV marginals, as we shall do hereinafter.”
Copula-based assimilation of radar and gauge information to derive bias-corrected precipitation fields (2012, background): “Further information about Copulas can be found e.g. in Joe (1997); Frees and Valdez (1998); Nelsen (1999)15 and Salvadori et al. (2007).”
Trivariate Frequency Analyses of Peak Discharge, Hydrograph Volume and Suspended Sediment Concentration Data Using Copulas (2014, methodology): “More information about these copula functions can be found in Joe (1997), Nelsen (1999) and Salvadori et al. (2007).”
Bivariate Flood Frequency Analysis with Historical Information Based on Copula (2013, methodology): “…: : : ;FmðxmÞ, it is possible to write an m-dimensional CDF with univariate marginals, F1ðx1Þ;F2ðx2Þ; : : : ;FmðxmÞ, as follows: Hðx1; x2; : : : ; xmÞ ¼ Cθ½F1ðx1Þ;F2ðx2Þ; : : : ;FmðxmÞ ð4Þ Different families of copulas have been proposed and described by Nelsen (2006) and Salvadori et al. (2007).”
Bivariate drought frequency analysis using the copula method (2012, methodology): “Salvadori et al. (2007) presented several environmental and geophysical examples by discussing univariate and multivariate extreme value theory, the copula approach, and the relationships between these two research areas.”
Copula based multisite model for daily precipitation simulation (2009, background): “The choice here is the multivari- 25 ate copula; only a short introduction on copulas is given here; readers interested in HESSD 6, 4485–4534, 2009 more general details are referred to (Joe, 1997), (Nelsen, 1999), or (Salvadori et al., 2007).”
A multivariate copula‐based framework for dealing with hazard scenarios and failure probabilities (2016, background): “The shape of a bivariate OR HS is illustrated in Figure 1a, considering the pair ðU; VÞ 2 I(2) (see, among others, Yue and Rasmussen [2002]; Shiau [2003], and also Salvadori [2004]; Salvadori and De Michele [2004]; De Michele et al.”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, background): “…which in turn corresponds to a separable STCS in the multiplicative form (on the condition that it is positive definite) ρ δ; τ; θð Þ ¼ FS δ; θSð Þ·FT τ; θTð Þ (19) For the Clayton copula in equation (17), the product copula corresponds to limiting case θ = 0 (Salvadori et al., 2007; p. 237).”
Distorted Copulas: Constructions and Tail Dependence (2010, methodology): “For an introduction to copula theory and some of its applications, we refer to Schweizer and Sklar (2006), Joe (1997), Nelsen (2006), McNeil, Frey, and Embrechts (2005), Salvadori et al. (2007).”
Copula-based statistical refinement of precipitation in RCM simulations over complex terrain (2011, methodology): “We follow the procedure of Salvadori et al.(2007) for the conditional simulation using Copulas.”
Multivariate return period calculation via survival functions (2013, methodology): “strategy introduced in Salvadori et al. [2011]. In practical words, we use the density f of F as a proxy of the likelihood of any realization over the survival critical layer of interest : then, we select the one that maximizes f, which may provide a ‘‘representative’’ design event.”
Multivariate quantiles in hydrological frequency analysis (2011, background): “For partial duration series, definitions are also available in the literature, e.g. in Shiau (2003) or Salvadori et al. (2007).”
Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas (2008, methodology): “Higher-order multivariate expressions can be formulated analogously [Nelsen, 2006; Salvadori et al., 2007].”
Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data (2010, background): “Genest and Favre (2007) discussed the various steps involved for investigating the dependence between two random variables (Salvadori et al. 2007).”
From Dependence to Causation (2016, background): “For contour plots of different parametric copulas, refer to (Salvadori et al., 2007).”