IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v34y1997i2p171-178.html
   My bibliography  Save this article

New characterization of Marshall-Olkin-type distributions via bivariate random summation scheme

Author

Listed:
  • Wu, Chufang

Abstract

We characterize the Marshall-Olkin distribution and extend it to a vast class of stable-Marshall-Olkin distributions. In particular, the Marshall-Olkin distribution will play the role of the limit in the law of large number for the bivariate geometric summation scheme, and the Laplace-Marshall-Olkin distribution will play the role of the normal distribution in the corresponding Central limit theorem. The rate of convergence is also studied.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:2:p:171-178
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(97)82790-3
    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.

    References listed on IDEAS

    as
    1. Resnick, Sidney & Greenwood, Priscilla, 1979. "A bivariate stable characterization and domains of attraction," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 206-221, June.
    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. 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.

    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. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(5), pages 912-951, October.
    2. Chan, Ngai Hang & Zhang, Rong-Mao, 2009. "Quantile inference for near-integrated autoregressive time series under infinite variance and strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4124-4148, December.
    3. Zhiyi Chi, 2018. "On a Multivariate Strong Renewal Theorem," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1235-1272, September.
    4. Cavaliere, Giuseppe & Georgiev, Iliyan, 2013. "Exploiting Infinite Variance Through Dummy Variables In Nonstationary Autoregressions," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1162-1195, December.
    5. Buraczewski, Dariusz & Dyszewski, Piotr & Iksanov, Alexander & Marynych, Alexander, 2020. "Random walks in a strongly sparse random environment," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 3990-4027.
    6. Jungjun Choi & In Choi, 2019. "Maximum likelihood estimation of autoregressive models with a near unit root and Cauchy errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1121-1142, October.
    7. Meerschaert, Mark M. & Scheffler, Hans-Peter, 1999. "Moment Estimator for Random Vectors with Heavy Tails," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 145-159, October.
    8. Mazur, Stepan & Otryakhin, Dmitry & Podolskij, Mark, 2018. "Estimation of the linear fractional stable motion," Working Papers 2018:3, Örebro University, School of Business.
    9. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
    10. repec:bot:quadip:118 is not listed on IDEAS
    11. Kozubowski, Tomasz J. & Meerschaert, Mark M. & Panorska, Anna K. & Scheffler, Hans-Peter, 2005. "Operator geometric stable laws," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 298-323, February.

    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:stapro:v:34:y:1997:i:2:p:171-178. 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.