Importance of tail dependence in bivariate frequency analysis

This paper highlights the importance of taking into account the tail dependence in the context of bivariate frequency analysis based on copulas. Three nonparametric estimators of the tail-dependence coefficient are compared by simulations with seven families of copulas. We choose the two estimators most adapted to a bivariate frequency analysis of the annual maximum flows and the corresponding flow hydrograph volumes of the Loire River (France). In this example, the bivariate return period and the conditional density of the volume given that the flow exceeds a given threshold are computed. The results show, as can be expected, that out of the seven copula families tested, five overestimate the return periods of correlated extreme events. These results bring to the forefront the importance of taking into account the tail dependence in order to estimate the risk adequately.