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Sharp constants in the Poisson approximation

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  • Roos, Bero

Abstract

We present some new sharp bounds for several distances between the Poisson binomial distribution and the Poisson law with the same mean. It is shown that the constants involved cannot be reduced.

Suggested Citation

  • Roos, Bero, 2001. "Sharp constants in the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 155-168, April.
    • Handle: RePEc:eee:stapro:v:52:y:2001:i:2:p:155-168
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    References listed on IDEAS

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    1. 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.
    2. Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    3. 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.
    4. Gerber, Hans U., 1984. "Error bounds for the compound poisson approximation," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 191-194, July.
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    Cited by:

    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. 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.
    3. Kruopis, Julius & Čekanavičius, Vydas, 2014. "Compound Poisson approximations for symmetric vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 30-42.
    4. 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.

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