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On the Gaussian representation of the Riesz probability distribution on symmetric matrices

Author

Listed:
  • Abdelhamid Hassairi

    (Laboratory of Probability and Statistics, Department of Mathematics, Faculty of Sciences of Sfax)

  • Fatma Ktari

    (Laboratory of Probability and Statistics, Department of Mathematics, Faculty of Sciences of Sfax)

  • Raoudha Zine

    (Laboratory of Probability and Statistics, Department of Mathematics, Faculty of Sciences of Sfax)

Abstract

The Riesz probability distribution on symmetric matrices represents an important extension of the Wishart distribution. It is defined by its Laplace transform involving the notion of generalized power. Based on the fact that some Wishart distributions are presented by the mean of the multivariate Gaussian distribution, it is shown that some Riesz probability distributions which are not necessarily Wishart are also presented by the mean of Gaussian samples with missing data. As a corollary, we deduce a Gaussian representation of the inverse Riesz distribution and we give its expectation. The results are assessed in simulation studies.

Suggested Citation

  • Abdelhamid Hassairi & Fatma Ktari & Raoudha Zine, 2022. "On the Gaussian representation of the Riesz probability distribution on symmetric matrices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 609-632, December.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:4:d:10.1007_s10182-022-00436-w
    DOI: 10.1007/s10182-022-00436-w
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    References listed on IDEAS

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    1. A. Hassairi & S. Lajmi, 2001. "Riesz Exponential Families on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 14(4), pages 927-948, October.
    2. W. B. Smith & R. R. Hocking, 1972. "Wishart Variate Generator," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(3), pages 341-345, November.
    3. Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    4. Andre Lucas & Anne Opschoor & Luca Rossini, 2021. "Tail Heterogeneity for Dynamic Covariance Matrices: the F-Riesz Distribution," Tinbergen Institute Discussion Papers 21-010/III, Tinbergen Institute, revised 11 Jul 2023.
    5. Hao, Jian & Krishnamoorthy, K., 2001. "Inferences on a Normal Covariance Matrix and Generalized Variance with Monotone Missing Data," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 62-82, July.
    6. Tounsi, Mariem & Zine, Raoudha, 2012. "The inverse Riesz probability distribution on symmetric matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 174-182.
    7. Andersson, Steen A. & Klein, Thomas, 2010. "On Riesz and Wishart distributions associated with decomposable undirected graphs," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 789-810, April.
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