Fully Nested 3-Copula: Procedure and Application on Hydrological Data

In multivariate frequency analysis, when the number of variables increases, different mutual structures of dependence among the analyzed quantities are usually observed. To correctly model this behavior, a very flexible joint distribution function is needed. A quite simple approach to build such distributions is based on the copula function. Precisely, using the so-called fully nested or asymmetric Archimedean copulas, it is possible not only to focus attention on the structures of dependence overlooking the margins—a property common to all copulas—but also to analyze more complex asymmetric structures of dependence. The aim of this paper is to describe the inference procedure to carry out a trivariate frequency analysis via asymmetric Archimedean copulas. The writers highlight the differences between the symmetric Archimedean copulas and asymmetric ones, show the inference procedure, and carefully describe some goodness- of-fit tests proposed in the literature to choose the best fitting model when one uses the fully nested Archimedean copulas. Finally, the methodology is applied to observed hydrological data, and results are shown and commented on.