IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v123y2014icp30-42.html
   My bibliography  Save this article

Compound Poisson approximations for symmetric vectors

Author

Listed:
  • Kruopis, Julius
  • Čekanavičius, Vydas

Abstract

Distribution of the sum of symmetric lattice vectors with supports on coordinate axes is approximated by multivariate compound Poisson distribution. The characteristic function and Kerstan’s methods are used to obtain local estimates and estimates in total variation.

Suggested Citation

  • Kruopis, Julius & Čekanavičius, Vydas, 2014. "Compound Poisson approximations for symmetric vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 30-42.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:30-42
    DOI: 10.1016/j.jmva.2013.08.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13001784
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.08.017?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. Vydas Čekanavičius & Bero Roos, 2006. "Compound binomial approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 815-815, December.
    2. 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.
    3. Roos, Bero, 2001. "Sharp constants in the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 155-168, April.
    4. Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    5. Novak, S. Y., 2003. "On the accuracy of multivariate compound Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 35-43, March.
    6. Deheuvels, Paul & Pfeifer, Dietmar, 1988. "Poisson approximations of multinomial distributions and point processes," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 65-89, April.
    7. 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.
    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.
    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. V. Čekanavičius & P. Vellaisamy, 2021. "Compound Poisson Approximations in $$\ell _p$$ ℓ p -norm for Sums of Weakly Dependent Vectors," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2241-2264, December.

    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. Novak, S.Y. & Xia, A., 2012. "On exceedances of high levels," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 582-599.
    2. Upadhye, N.S. & Vellaisamy, P., 2013. "Improved bounds for approximations to compound distributions," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 467-473.
    3. A. Elijio & V. Čekanavičius, 2015. "Compound Poisson approximation to weighted sums of symmetric discrete variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 195-210, February.
    4. Roos, Bero, 2001. "Sharp constants in the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 155-168, April.
    5. 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.
    6. Salazar García, Juan Fernando & Guzmán Aguilar, Diana Sirley & Hoyos Nieto, Daniel Arturo, 2023. "Modelación de una prima de seguros mediante la aplicación de métodos actuariales, teoría de fallas y Black-Scholes en la salud en Colombia [Modelling of an insurance premium through the application," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 35(1), pages 330-359, June.
    7. 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.
    8. N. S. Upadhye & P. Vellaisamy, 2014. "Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 951-968, December.
    9. Marco Faravelli & Priscilla Man, 2021. "Generalized majority rules: utilitarian welfare in large but finite populations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(1), pages 21-48, July.
    10. Vijay Krishna & John Morgan, 2015. "Majority Rule and Utilitarian Welfare," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 339-375, November.
    11. Gan, H.L. & Xia, A., 2015. "Stein’s method for conditional compound Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 19-26.
    12. 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.
    13. Vishal Gupta & Nathan Kallus, 2022. "Data Pooling in Stochastic Optimization," Management Science, INFORMS, vol. 68(3), pages 1595-1615, March.
    14. Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    15. Krishna, Vijay & Morgan, John, 2012. "Voluntary voting: Costs and benefits," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2083-2123.

    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:123:y:2014:i:c:p:30-42. 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.