IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v82y1999i2p205-227.html
   My bibliography  Save this article

Signed Poisson approximations for Markov chains

Author

Listed:
  • Cekanavicius, V.
  • Mikalauskas, M.

Abstract

Consider a sum of Markov dependent lattice variables. The normal approximation is trivial for this sum if the total variation distance is considered. Replacement of the normal approximation by its Poisson structured analogue changes the situation radically. Moreover, considering the Markov binomial distribution we prove that signed Poisson approximation can be more accurate than both the normal and Poisson approximations. Possible improvements due to asymptotic expansions are discussed.

Suggested Citation

  • Cekanavicius, V. & Mikalauskas, M., 1999. "Signed Poisson approximations for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 205-227, August.
    • Handle: RePEc:eee:spapps:v:82:y:1999:i:2:p:205-227
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00017-4
    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. Hipp, Christian, 1986. "Improved Approximations for the Aggregate Claims Distribution in the Individual Model," ASTIN Bulletin, Cambridge University Press, vol. 16(2), pages 89-100, November.
    2. Borovkov, K. A. & Pfeifer, D., 1996. "Pseudo-Poisson approximation for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 163-180, January.
    3. Kuon, S. & Reich, A. & Reimers, L., 1987. "Panjer vs Kornya vs De Pril: A Comparison from a Practical Point of View," ASTIN Bulletin, Cambridge University Press, vol. 17(2), pages 183-191, 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. 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.
    2. A. D. Barbour & Torgny Lindvall, 2006. "Translated Poisson Approximation for Markov Chains," Journal of Theoretical Probability, Springer, vol. 19(3), pages 609-630, December.
    3. Cekanavicius, V., 2002. "On the convergence of Markov binomial to Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 83-91, May.

    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. Ribas, Carme & Marin-Solano, Jesus & Alegre, Antonio, 2003. "On the computation of the aggregate claims distribution in the individual life model with bivariate dependencies," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 201-215, April.
    2. Cekanavicius, V., 1998. "Poisson approximations for sequences of random variables," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 101-107, August.
    3. Cekanavicius, V., 1996. "On multivariate Le Cam theorem and compound Poisson measures," Statistics & Probability Letters, Elsevier, vol. 28(1), pages 33-39, June.
    4. Roos, Bero, 2007. "On variational bounds in the compound Poisson approximation of the individual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 403-414, May.
    5. Yang, Jingping & Zhou, Shulin & Zhang, Zhenyong, 2005. "The compound Poisson random variable's approximation to the individual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 57-77, February.
    6. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.

    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:82:y:1999:i:2:p:205-227. 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.