IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v29y1989i1p155-162.html
   My bibliography  Save this article

A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model

Author

Listed:
  • Sutradhar, Brajendra C.
  • Ali, Mir M.

Abstract

We consider the elliptical distribution of n p-dimensional random vectors X1, ..., Xn having p.d.f. of the form k(n, p) [Lambda]-n/2 g([Sigma]j=1n(Xj-[theta])' [Lambda]-1(Xj-[theta])) as a generalization of the multivariate normal distribution. Let A denote the Wishart matrix defined by , where the vector is given by . In this paper we derive the distribution of A when X1, ..., Xn is assumed to have an elliptical distribution. This result is specialized to the case where X1, ..., Xn is assumed to have a multivariate t distribution, a subclass of the elliptical class of distributions. Furthermore, the first two moments of A for this subclass is computed.

Suggested Citation

  • Sutradhar, Brajendra C. & Ali, Mir M., 1989. "A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 155-162, April.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:1:p:155-162
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(89)90082-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Kibria, B. M. Golam & Haq, M. Safiul, 1999. "Predictive Inference for the Elliptical Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 235-249, February.
    2. Bodnar, Olha & Bodnar, Taras, 2021. "Objective Bayesian meta-analysis based on generalized multivariate random effects model," Working Papers 2021:5, Örebro University, School of Business.
    3. Guo, Junhao & Zhou, Jie & Hu, Sanfeng, 2020. "Intrinsic covariance matrix estimation for multivariate elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 162(C).
    4. Ogasawara, Haruhiko, 2023. "The density of the sample correlations under elliptical symmetry with or without the truncated variance-ratio," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    5. A. Batsidis & K. Zografos, 2006. "Discrimination of Observations into One of Two Elliptic Populations based on Monotone Training Samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 221-241, October.
    6. Brajendra C. Sutradhar, 2022. "Fixed versus Mixed Effects Based Marginal Models for Clustered Correlated Binary Data: an Overview on Advances and Challenges," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 259-302, May.
    7. Fang, B.Q., 2008. "Noncentral matrix quadratic forms of the skew elliptical variables," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1105-1127, July.
    8. Kibria, B.M. Golam, 2006. "The matrix-t distribution and its applications in predictive inference," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 785-795, March.
    9. Micheas, Athanasios C. & Dey, Dipak K., 2005. "Modeling shape distributions and inferences for assessing differences in shapes," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 257-280, February.
    10. Fang, B.Q., 2006. "Sample mean, covariance and T2 statistic of the skew elliptical model," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1675-1690, August.
    11. Bekker, Andriëtte & van Niekerk, Janet & Arashi, Mohammad, 2017. "Wishart distributions: Advances in theory with Bayesian application," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 272-283.

    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:29:y:1989:i:1:p:155-162. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.