On the estimation of multivariate tail probabilities.

Summary This thesis presents contributions to multivariate modeling of distribution tails. We introduce a new modeling of the joint tail probabilities of a multivariate distribution with Pareto margins. This model is inspired by Wadsworth and Tawn (2013). A new non-standard regular multivariate variation of coefficient a bivariate function is introduced, allowing to generalize two modeling approaches respectively proposed by Ramos and Ledford (2009)and Wadsworth and Tawn (2013). Building on this modeling we propose a new class of semi-parametric models for multivariate extrapolation along paths spanning the entire first positive quadrant. We also consider parametric models built with a non-negative measure satisfying a constraint that generalizes that of Ramos and Ledford (2009). These new models are flexible and suitable for both dependence and asymptotic independence situations.