IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v24y1988i1p109-122.html
   My bibliography  Save this article

Some families of mutivariate symmetric distributions related to exponential distribution

Author

Listed:
  • Fang, Kai-Tai
  • Fang, Bi-Qi

Abstract

This paper introduces a family of multivariate symmetric distributions, which includes the one with i.i.d. exponential components as its special member. This family, denoted by Fn, is defined as scale mixtures of the uniform distribution on the surface of the l1 unit sphere and studied from several aspects such as distribution functions, probability density functions, marginal and conditional distributions and components' independence. A more general family Tn in which the survival functions are functions in l1 norm and an important subset Dn,[infinity] of scale mixtures of random vector with i.i.d. exponential components are also discussed. The relationships among these three families and some applications are given.

Suggested Citation

  • Fang, Kai-Tai & Fang, Bi-Qi, 1988. "Some families of mutivariate symmetric distributions related to exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 109-122, January.
    • Handle: RePEc:eee:jmvana:v:24:y:1988:i:1:p:109-122
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(88)90105-4
    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. Yanqin Fan & Marc Henry, 2020. "Vector copulas," Papers 2009.06558, arXiv.org, revised Apr 2021.
    2. Jiajuan Liang & Kai-Tai Fang & Fred Hickernell, 2008. "Some necessary uniform tests for spherical symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 679-696, September.
    3. Hélène Cossette & Etienne Marceau & Quang Huy Nguyen & Christian Y. Robert, 2019. "Tail Approximations for Sums of Dependent Regularly Varying Random Variables Under Archimedean Copula Models," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 461-490, June.
    4. Claude Lefèvre & Matthieu Simon, 2021. "Schur-Constant and Related Dependence Models, with Application to Ruin Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 317-339, March.
    5. Yue, Xinnian & Ma, Chunsheng, 1995. "Multivariate p-norm symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 281-288, September.
    6. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
    7. Ng, Kai Wang & Tian, Guo-Liang, 2001. "Characteristic Functions of 1-Spherical and 1-Norm Symmetric Distributions and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 192-213, February.
    8. Qu, Xiaomei & Zhou, Jie & Shen, Xiaojing, 2010. "Archimedean copula estimation and model selection via l1-norm symmetric distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 406-414, April.
    9. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
    10. Fang, B. Q., 2002. "Estimation of the location parameter of the l1-norm symmetric matrix variate distributions," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 269-280, April.

    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:24:y:1988:i:1:p:109-122. 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.