Semi-parametric approximation of Kendall's distribution function and multivariate Return Periods

In this work we outline a constructive approach for the approximation of Kendall's distribution function and Kendall's Return Period in the bivariate case. First, we introduce a suitable theoretical framework, based on the Theory of Copulas, where to embed the issue. Then, we outline an original construction procedure to approximate the empirical Kendall distribution function estimated using the available data. The whole approach is semi-parametric: the empirical Kendall distribution function is approximated via a (suitable) continuous piece-wise linear function on the unit interval. A sensitivity analysis is carried out via a simulation procedure, in order to investigate the robustness of the approach proposed against several relevant factors.