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

Gianfausto Salvadori, Fabrizio Durante, Elisa Perrone

Résumé


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.

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Creative Commons License
Ce travail est autorisé sous licence avec la Licence de paternité Creative Commons 3.0.

SFdS / SMF - Journal de la Société Française de Statistique - ISSN 2102-6238