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The inverse Riesz probability distribution on symmetric matrices

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  • Tounsi, Mariem
  • Zine, Raoudha

Abstract

The Riesz distributions on positive definite symmetric matrices are used to introduce a class of inverse Riesz distributions. Some fundamental properties of these new distributions are established. We prove a property of independence between blocks of an inverse Riesz matrix, and we show that some projections of these distributions are also inverse Riesz. We also show the relationship between these distributions with the Riesz inverse Gaussian distributions introduced by Hassairi et al. (2007) [7].

Suggested Citation

  • Tounsi, Mariem & Zine, Raoudha, 2012. "The inverse Riesz probability distribution on symmetric matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 174-182.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:174-182
    DOI: 10.1016/j.jmva.2012.05.013
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    References listed on IDEAS

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    1. Harrar, Solomon W. & Seneta, Eugene & Gupta, Arjun K., 2006. "Duality between matrix variate t and matrix variate V.G. distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1467-1475, July.
    2. Massam, Hélène & Wesolowski, Jacek, 2006. "The Matsumoto-Yor property and the structure of the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 103-123, January.
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    Cited by:

    1. 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.
    2. 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.
    3. Kammoun, Kaouthar & Louati, Mahdi & Masmoudi, Afif, 2017. "Maximum likelihood estimator of the scale parameter for the Riesz distribution," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 127-131.
    4. Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    5. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.
    6. Mariem Tounsi, 2020. "The Extended Matrix-Variate Beta Probability Distribution on Symmetric Matrices," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 647-676, June.
    7. Anne Opschoor & Dewi Peerlings & Luca Rossini & Andre Lucas, 2024. "Density Forecasting for Electricity Prices under Tail Heterogeneity with the t-Riesz Distribution," Tinbergen Institute Discussion Papers 24-049/III, Tinbergen Institute.

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