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On a construction of multivariate distributions given some multidimensional marginals

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01575169
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Submitted on : Friday, March 1, 2019 - 3:00:40 PM
Last modification on : Wednesday, February 17, 2021 - 11:48:02 AM

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Nabil Kazi-Tani, Didier Rullière. On a construction of multivariate distributions given some multidimensional marginals. Advances in Applied Probability, Applied Probability Trust, 2019, 51 (2), pp.487-513. ⟨10.1017/apr.2019.14⟩. ⟨hal-01575169v3⟩

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