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Recent developments of statistical tools for hydrological application
... Recent developments in environmental statistics have shown the great potential of copulas in a multivariate risk assessment framework (see, for instance, [1,4]). In the traditional structural approach, the response Y = (Y 1 , . . . ...
In environmental applications, the estimation of the structural risk is crucial. A statistical model for the behavior of the input variables is generally required, possibly accounting for different dependence structures among such variables. Copulas represent a suitable tool for dealing with natural extremes and non-linear dependencies. Two semi-parametric procedures for the approximation of, respectively, Extreme Value and Archimedean copulas, are proposed in order to provide a model for the estimation of the structural risk. The approximating techniques are evaluated by Monte Carlo tests, and illustrated via a case study concerning a preliminary rubble mound breakwater design.
... Copulas supply the theoretical framework for performing multivariate risk assessment and rational decision-making in various applications, e.g. in finance (see, among others, McNeil et al. 2005;Malevergne and Sornette 2006;Jaworski et al. 2013) as well as in environmental sciences (see Salvadori et al. 2007;Grimaldi et al. 2009 for a review, and Kazianka and Pilz 2010; Carnicero et al. 2013;Durante and Okhrin 2015;Ming et al. 2015;Saad et al. 2015 for some recent advances). ...
In environmental applications, the estimation of the structural risk is fundamental. Beside the knowledge of the physical response of the structure to the loads of interest, a statistical model for the behavior of the input variables is generally required, possibly accounting for the fact that these variables are usually non-independent. For this purpose, a multivariate approach based on copulas is adopted in this paper. In particular, the following classes of dependence structures are often used in practice: the Extreme Value copulas, and the Archimedean copulas. However, how to properly select a suitable Extreme Value or Archimedean copula is a problem open to many solutions. As a viable one, this work shows how two semi-parametric approximations to, respectively, Extreme Value and Archimedean copulas, can be used in order to circumvent the troublesome selection issue in the estimation of the structural risk. Suitable simulation studies are performed, in order to check and evaluate the performance of the approximating techniques introduced in this work.
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