On a construction of multivariate distributions given some multidimensional marginals
Résumé
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 conditions that are easy to verify, to ensure that a given construction is projective. We illustrate our results on elliptical distributions on the first hand, and on a new class of distribution having given bivariate exponential margins on the other hand.
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