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Compound Poisson approximations for symmetric vectors

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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