Spin-off Extreme Value and Archimedean copulas for estimating the bivariate structural risk
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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.