IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v113y2013icp48-58.html
   My bibliography  Save this article

Scale mixtures of Kotz–Dirichlet distributions

Author

Listed:
  • Balakrishnan, N.
  • Hashorva, E.

Abstract

In this paper, we first show that a k-dimensional Dirichlet random vector has independent components if and only if it is a Kotz Type I Dirichlet random vector. We then consider in detail the class of k-dimensional scale mixtures of Kotz–Dirichlet random vectors, which is a natural extension of the class of Kotz Type I random vectors. An interesting member of the Kotz–Dirichlet class of multivariate distributions is the family of Pearson–Kotz Dirichlet distributions, for which we present a new distributional property. In an asymptotic framework, we show that the Kotz Type I Dirichlet distributions approximate the conditional distributions of scale mixtures of Kotz–Dirichlet random vectors. Furthermore, we show that the tail indices of regularly varying Dirichlet random vectors can be expressed in terms of the Kotz Type I Dirichlet random vectors.

Suggested Citation

  • Balakrishnan, N. & Hashorva, E., 2013. "Scale mixtures of Kotz–Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 48-58.
    • Handle: RePEc:eee:jmvana:v:113:y:2013:i:c:p:48-58
    DOI: 10.1016/j.jmva.2011.08.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X11001710
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2011.08.012?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. Thomas Mikosch, 2005. "How to model multivariate extremes if one must?," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 324-338, August.
    2. Davis, Richard & Resnick, Sidney, 1988. "Extremes of moving averages of random variables from the domain of attraction of the double exponential distribution," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 41-68, November.
    3. Hashorva, Enkelejd, 2008. "Conditional limiting distribution of beta-independent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1438-1459, August.
    4. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    5. 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.
    6. Rinya Takahashi & Masaaki Sibuya, 1998. "Prediction of the Maximum Size in Wicksell's Corpuscle Problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 361-377, June.
    7. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
    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. Arendarczyk, Marek & Kozubowski, Tomasz. J. & Panorska, Anna K., 2018. "The joint distribution of the sum and maximum of dependent Pareto risks," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 136-156.
    2. Hashorva, Enkelejd, 2015. "Extremes of aggregated Dirichlet risks," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 334-345.

    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. Balakrishnan, N. & Hashorva, E., 2011. "On Pearson-Kotz Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 948-957, May.
    2. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.
    3. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    4. 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.
    5. Muchmore Patrick & Marjoram Paul, 2015. "Exact likelihood-free Markov chain Monte Carlo for elliptically contoured distributions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(4), pages 317-332, August.
    6. 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.
    7. Hashorva, Enkelejd, 2006. "On the regular variation of elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1427-1434, August.
    8. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
    9. Maume-Deschamps, V. & Rullière, D. & Usseglio-Carleve, A., 2017. "Quantile predictions for elliptical random fields," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 1-17.
    10. Singh, Vikas Vikram & Lisser, Abdel, 2019. "A second-order cone programming formulation for two player zero-sum games with chance constraints," European Journal of Operational Research, Elsevier, vol. 275(3), pages 839-845.
    11. Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.
    12. Hashorva, Enkelejd, 2015. "Extremes of aggregated Dirichlet risks," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 334-345.
    13. Zhang, Ran & Czado, Claudia & Min, Aleksey, 2011. "Efficient maximum likelihood estimation of copula based meta t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1196-1214, March.
    14. Nolde, Natalia, 2014. "Geometric interpretation of the residual dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 85-95.
    15. Geluk, J.L. & De Vries, C.G., 2006. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
    16. Falk, Michael, 1998. "A Note on the Comedian for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 306-317, November.
    17. Viktor Beneš & Karel Bodlák & Daniel Hlubinka, 2003. "Stereology of Extremes; Bivariate Models and Computation," Methodology and Computing in Applied Probability, Springer, vol. 5(3), pages 289-308, September.
    18. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    19. Jacob, P. & Suquet, Ch., 1997. "Regression and asymptotical location of a multivariate sample," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 173-179, September.
    20. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.

    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:113:y:2013:i:c:p:48-58. 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.