IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v111y2012icp174-182.html
   My bibliography  Save this article

The inverse Riesz probability distribution on symmetric matrices

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1200139X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.05.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Matsumoto, Hiroyuki & Wesolowski, Jacek & Witkowski, Piotr, 2009. "Tree structured independence for exponential Brownian functionals," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3798-3815, October.
    2. Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2013. "On the exact and approximate distributions of the product of a Wishart matrix with a normal vector," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 70-81.
    3. Wesolowski, Jacek & Witkowski, Piotr, 2007. "Hitting times of Brownian motion and the Matsumoto-Yor property on trees," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1303-1315, September.
    4. V. Seshadri & J. Wesołowski, 2008. "More on connections between Wishart and matrix GIG distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 219-232, September.
    5. Kozubowski, Tomasz J. & Mazur, Stepan & Podgorski, Krysztof, 2022. "Matrix Variate Generalized Laplace Distributions," Working Papers 2022:7, Örebro University, School of Business.
    6. Wesołowski, Jacek, 2015. "On the Matsumoto–Yor type regression characterization of the gamma and Kummer distributions," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 145-149.
    7. Bobecka, Konstancja, 2015. "The Matsumoto–Yor property on trees for matrix variates of different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 22-34.
    8. Piliszek, Agnieszka & Wesołowski, Jacek, 2016. "Kummer and gamma laws through independences on trees—Another parallel with the Matsumoto–Yor property," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 15-27.
    9. Kozubowski, Tomasz J. & Mazur, Stepan & Podgórski, Krzysztof, 2022. "Matrix Gamma Distributions and Related Stochastic Processes," Working Papers 2022:12, Örebro University, School of Business.
    10. Fung, Thomas & Seneta, Eugene, 2010. "Extending the multivariate generalised t and generalised VG distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 154-164, January.
    11. Bartosz Kołodziejek, 2017. "The Matsumoto–Yor Property and Its Converse on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 30(2), pages 624-638, June.
    12. Letac, Gérard & Wesołowski, Jacek, 2020. "Multivariate reciprocal inverse Gaussian distributions from the Sabot–Tarrès–Zeng integral," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    13. Koudou, Angelo Efoevi, 2012. "A Matsumoto–Yor property for Kummer and Wishart random matrices," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1903-1907.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:174-182. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.