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On a construction of multivariate distributions given some multidimensional marginals

Part of: Distribution theory - Probability Multivariate analysis

Published online by Cambridge University Press:  07 August 2019

Nabil Kazi-Tani  and
Didier Rullière
Nabil Kazi-Tani*
Affiliation:
Université Lyon 1
Didier Rullière*
Affiliation:
Université Lyon 1
*
*Postal address: Laboratoire SAF, ISFA, Université Lyon 1, 50 Avenue Tony Garnier, F-69366 Lyon Cedex 07, France.
*Postal address: Laboratoire SAF, ISFA, Université Lyon 1, 50 Avenue Tony Garnier, F-69366 Lyon Cedex 07, France.
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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 does 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

Multidimensional marginalcopulaelliptical distribution

MSC classification

Primary: 60E05: Distributions 60E10: Characteristic functions; other transforms
Secondary: 62H05: Characterization and structure theory 62H20: Measures of association (correlation, canonical correlation, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 2 , June 2019 , pp. 487 - 513
Copyright
© Applied Probability Trust 2019 

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