On a construction of multivariate distributions given some multidimensional marginals

Nabil Kazi-Tani (1) , Didier Rullière (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière

In this paper, we investigate the link between the joint law of a d-dimensional random vector and the law of some of its multivariate marginals. We introduce and focus on a class of distributions, that we call projective, for which we give detailed properties. This allows us to obtain necessary conditions for a given construction to be projective. We illustrate our results by proposing some theoretical projective distributions, as elliptical distributions or a new class of distribution having given bivariate margins. In the case where the data do not necessarily correspond to a projective distribution, we also explain how to build proper distributions while checking that the distance to the prescribed projections is small enough.

Mots clés: Copulas; Multidimensional marginals; Elliptical Distributions

Domaines: Economies et finances; Probabilités [math.PR]; Statistiques [math.ST]

Nabil Kazi-Tani, Didier Rullière. On a construction of multivariate distributions given some multidimensional marginals. 2017. ⟨hal-01575169v2⟩