IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i1p190-207.html
   My bibliography  Save this article

Poisson type approximations for the Markov binomial distribution

Author

Listed:
  • Cekanavicius, Vydas
  • Roos, Bero

Abstract

The Markov binomial distribution is approximated by the Poisson distribution with the same mean, by a translated Poisson distribution and by two-parametric Poisson type signed measures. Using an adaptation of Le Cam's operator technique, estimates of accuracy are proved for the total variation, local and Wasserstein norms. In a special case, asymptotically sharp constants are obtained. For some auxiliary results, we used Stein's method.

Suggested Citation

  • Cekanavicius, Vydas & Roos, Bero, 2009. "Poisson type approximations for the Markov binomial distribution," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 190-207, January.
  • Handle: RePEc:eee:spapps:v:119:y:2009:i:1:p:190-207
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00016-1
    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. P. Deheuvels & D. Pfeifer, 1988. "On a relationship between Uspensky's theorem and poisson approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 671-681, December.
    2. Roos, Bero, 2001. "Sharp constants in the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 155-168, April.
    3. Ourania Chryssaphinou & Eutichia Vaggelatou, 2002. "Compound Poisson Approximation for Multiple Runs in a Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 411-424, June.
    4. Cekanavicius, V. & Mikalauskas, M., 1999. "Signed Poisson approximations for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 205-227, August.
    Full references (including those not matched with items on IDEAS)

    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. Kruopis, Julius & Čekanavičius, Vydas, 2014. "Compound Poisson approximations for symmetric vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 30-42.
    2. Roos, Bero, 1995. "A semigroup approach to poisson approximation with respect to the point metric," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 305-314, September.
    3. Roos, Bero, 2001. "Sharp constants in the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 155-168, April.
    4. A. D. Barbour & Torgny Lindvall, 2006. "Translated Poisson Approximation for Markov Chains," Journal of Theoretical Probability, Springer, vol. 19(3), pages 609-630, December.
    5. Novak, S.Y. & Xia, A., 2012. "On exceedances of high levels," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 582-599.
    6. Cekanavicius, V., 2002. "On the convergence of Markov binomial to Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 83-91, May.
    7. Milienos, F.S. & Koutras, M.V., 2008. "A lower bound for the reliability function of multiple failure mode systems," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1639-1648, September.
    8. Vydas Čekanavičius & Bero Roos, 2006. "Compound Binomial Approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 187-210, 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:spapps:v:119:y:2009:i:1:p:190-207. 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/505572/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.