IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v16y2014i1d10.1007_s11009-012-9297-4.html
   My bibliography  Save this article

Multivariate Generalized Marshall–Olkin Distributions and Copulas

Author

Listed:
  • Jianhua Lin

    (Xiamen University)

  • Xiaohu Li

    (Xiamen University)

Abstract

The multivariate generalized Marshall–Olkin distributions, which include the multivariate Marshall–Olkin exponential distribution due to Marshall and Olkin (J Am Stat Assoc 62:30–41, 1967) and multivariate Marshall–Olkin type distribution due to Muliere and Scarsini (Ann Inst Stat Math 39:429–441, 1987) as special cases, are studied in this paper. We derive the survival copula and the upper/lower orthant dependence coefficient, build the order of these survival copulas, and investigate the evolution of dependence of the residual life with respect to age. The main conclusions developed here are both nice extensions of the main results in Li (Commun Stat Theory Methods 37:1721–1733, 2008a, Methodol Comput Appl Probab 10:39–54, 2008b) and high dimensional generalizations of some results on the bivariate generalized Marshall–Olkin distributions in Li and Pellerey (J Multivar Anal 102:1399–1409, 2011).

Suggested Citation

  • Jianhua Lin & Xiaohu Li, 2014. "Multivariate Generalized Marshall–Olkin Distributions and Copulas," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 53-78, March.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:1:d:10.1007_s11009-012-9297-4
    DOI: 10.1007/s11009-012-9297-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-012-9297-4
    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/s11009-012-9297-4?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. Marco Scarsini & Pietro Muliere, 1987. "Characterization of a Marshall-Olkin type class of distributions," Post-Print hal-00542248, HAL.
    2. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
    3. Mai, Jan-Frederik & Scherer, Matthias, 2010. "The Pickands representation of survival Marshall-Olkin copulas," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 357-360, March.
    4. Li, Xiaohu & Pellerey, Franco, 2011. "Generalized Marshall-Olkin distributions and related bivariate aging properties," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1399-1409, November.
    5. Wu, Chufang, 1997. "New characterization of Marshall-Olkin-type distributions via bivariate random summation scheme," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 171-178, June.
    6. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    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. Umberto Cherubini & Sabrina Mulinacci, 2021. "Hierarchical Archimedean Dependence in Common Shock Models," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 143-163, March.
    2. Sabrina Mulinacci, 2022. "A Marshall-Olkin Type Multivariate Model with Underlying Dependent Shocks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2455-2484, December.
    3. Gobbi, Fabio & Kolev, Nikolai & Mulinacci, Sabrina, 2021. "Ryu-type extended Marshall-Olkin model with implicit shocks and joint life insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 342-358.
    4. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
    5. Sloot Henrik, 2020. "The deFinetti representation of generalised Marshall–Olkin sequences," Dependence Modeling, De Gruyter, vol. 8(1), pages 107-118, 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. Matthias Scherer & Henrik Sloot, 2019. "Exogenous shock models: analytical characterization and probabilistic construction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 931-959, November.
    2. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
    3. Sloot Henrik, 2020. "The deFinetti representation of generalised Marshall–Olkin sequences," Dependence Modeling, De Gruyter, vol. 8(1), pages 107-118, January.
    4. Umberto Cherubini & Sabrina Mulinacci, 2021. "Hierarchical Archimedean Dependence in Common Shock Models," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 143-163, March.
    5. Haijun Li, 2008. "Tail Dependence Comparison of Survival Marshall–Olkin Copulas," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 39-54, March.
    6. Li, Yang & Sun, Jianguo & Song, Shuguang, 2012. "Statistical analysis of bivariate failure time data with Marshall–Olkin Weibull models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2041-2050.
    7. Sloot Henrik, 2020. "The deFinetti representation of generalised Marshall–Olkin sequences," Dependence Modeling, De Gruyter, vol. 8(1), pages 107-118, January.
    8. Bedoui, Rihab & Braiek, Sana & Guesmi, Khaled & Chevallier, Julien, 2019. "On the conditional dependence structure between oil, gold and USD exchange rates: Nested copula based GJR-GARCH model," Energy Economics, Elsevier, vol. 80(C), pages 876-889.
    9. Zhang, Dalu, 2014. "Vine copulas and applications to the European Union sovereign debt analysis," International Review of Financial Analysis, Elsevier, vol. 36(C), pages 46-56.
    10. Ozonder, Gozde & Miller, Eric J., 2021. "Longitudinal investigation of skeletal activity episode timing decisions – A copula approach," Journal of choice modelling, Elsevier, vol. 40(C).
    11. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    12. Yu, Lining & Voit, Eberhard O., 2006. "Construction of bivariate S-distributions with copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1822-1839, December.
    13. John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
    14. Nabil Kazi-Tani & Didier Rullière, 2019. "On a construction of multivariate distributions given some multidimensional marginals," Post-Print hal-01575169, HAL.
    15. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 22(2), pages 98-134.
    16. Takaaki Koike & Mihoko Minami, 2017. "Estimation of Risk Contributions with MCMC," Papers 1702.03098, arXiv.org, revised Jan 2019.
    17. Aristidis K. Nikoloulopoulos & Peter G. Moffatt, 2019. "Coupling Couples With Copulas: Analysis Of Assortative Matching On Risk Attitude," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 654-666, January.
    18. 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.
    19. Yuri Salazar & Wing Ng, 2015. "Nonparametric estimation of general multivariate tail dependence and applications to financial time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 121-158, March.
    20. Szabolcs Majoros & Andr'as Zempl'eni, 2018. "Multivariate stable distributions and their applications for modelling cryptocurrency-returns," Papers 1810.09521, arXiv.org.

    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:16:y:2014:i:1:d:10.1007_s11009-012-9297-4. 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.