IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i4d10.1007_s11009-020-09817-7.html
   My bibliography  Save this article

A New Class of Multivariate Elliptically Contoured Distributions with Inconsistency Property

Author

Listed:
  • Yeshunying Wang

    (Qufu Normal University)

  • Chuancun Yin

    (Qufu Normal University)

Abstract

We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal distributions, conditional distributions, linear transformations, characteristic functions and dependence measure in the perspective of the inconsistency property. In addition, we provide a real data example to show that the new distributions have reasonable flexibility.

Suggested Citation

  • Yeshunying Wang & Chuancun Yin, 2021. "A New Class of Multivariate Elliptically Contoured Distributions with Inconsistency Property," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1377-1407, December.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09817-7
    DOI: 10.1007/s11009-020-09817-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-020-09817-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-020-09817-7?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. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2018. "A multivariate tail covariance measure for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 27-35.
    2. Indranil Ghosh & Ayman Alzaatreh, 2018. "A new class of generalized logistic distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(9), pages 2043-2055, May.
    3. Liang, Jia-Juan & Bentler, Peter M., 1998. "Characterizations of some subclasses of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 155-164, September.
    4. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    5. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    6. Kotz, S. & Ostrovskii, I., 1994. "Characteristic Functions of a Class of Elliptic Distributions," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 164-178, April.
    7. Ali, Mir M. & Mikhail, N. N. & Haq, M. Safiul, 1978. "A class of bivariate distributions including the bivariate logistic," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 405-412, September.
    8. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    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. Liebscher Eckhard, 2023. "Constructing models for spherical and elliptical densities," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-19, January.

    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. Victor Korolev, 2020. "Some Properties of Univariate and Multivariate Exponential Power Distributions and Related Topics," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    2. Chuancun Yin, 2019. "Stochastic ordering of Gini indexes for multivariate elliptical random variables," Papers 1908.01943, arXiv.org, revised Sep 2019.
    3. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    4. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    5. Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.
    6. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 15/13, Institute for Fiscal Studies.
    7. V. Maume-Deschamps & D. Rullière & A. Usseglio-Carleve, 2018. "Spatial Expectile Predictions for Elliptical Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 643-671, June.
    8. Baishuai Zuo & Chuancun Yin, 2020. "Conditional tail risk expectations for location-scale mixture of elliptical distributions," Papers 2007.09350, arXiv.org.
    9. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
    10. Shushi, Tomer, 2019. "The Minkowski length of a spherical random vector," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 104-107.
    11. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.
    12. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.
    13. Hashorva, Enkelejd, 2006. "On the regular variation of elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1427-1434, August.
    14. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 41/13, Institute for Fiscal Studies.
    15. Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.
    16. Hashorva, Enkelejd, 2007. "Conditional limiting distribution of Type III elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 282-294, February.
    17. Fotopoulos, Stergios B., 2017. "Symmetric Gaussian mixture distributions with GGC scales," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 185-194.
    18. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    19. Deepak K. Jadhav & Ramanathan Thekke Variyam, 2023. "Modified Expected Shortfall: a Coherent Risk Measure for Elliptical Family of Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 234-256, May.
    20. Jaworski, Piotr & Pitera, Marcin, 2017. "A note on conditional covariance matrices for elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 230-235.

    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:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09817-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.