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On a construction of multivariate distributions given some multidimensional marginals

Nabil Kazi-Tani () and Didier Rulliere ()
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Nabil Kazi-Tani: SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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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.

Keywords: Copulas; Multidimensional marginals; Elliptical Distributions (search for similar items in EconPapers)
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Date: 2019-08-07
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01575169v3
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Published in Advances in Applied Probability, Applied Probability Trust, 2019, 51 (2), pp.487-513. ⟨https://doi.org/10.1017/apr.2019.14⟩. ⟨10.1017/apr.2019.14⟩

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