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On a construction of multivariate distributions given some multidimensional marginals

Author

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  • Nabil Kazi-Tani

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Didier Rullière

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

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.

Suggested Citation

  • Nabil Kazi-Tani & Didier Rullière, 2019. "On a construction of multivariate distributions given some multidimensional marginals," Post-Print hal-01575169, HAL.
    • Handle: RePEc:hal:journl:hal-01575169
    DOI: 10.1017/apr.2019.14
    Note: View the original document on HAL open archive server: https://hal.science/hal-01575169v3
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    References listed on IDEAS

    as
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    Keywords

    Copulas; Multidimensional marginals; Elliptical Distributions;
    All these keywords.

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