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On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law

Author

Listed:
  • Sergei Nagaev

    (Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

  • Vladimir Chebotarev

    (Computing Center, Far Eastern Branch of the Russian Academy of Sciences, 680000 Khabarovsk, Russia
    These authors contributed equally to this work.)

Abstract

A subject of this study is the behavior of the tail of the binomial distribution in the case of the Poisson approximation. The deviation from unit of the ratio of the tail of the binomial distribution and that of the Poisson distribution, multiplied by the correction factor, is estimated. A new type of approximation is introduced when the parameter of the approximating Poisson law depends on the point at which the approximation is performed. Then the transition to the approximation by the Poisson law with the parameter equal to the mathematical expectation of the approximated binomial law is carried out. In both cases error estimates are obtained. A number of conjectures are made about the refinement of the known estimates for the Kolmogorov distance between binomial and Poisson distributions.

Suggested Citation

  • Sergei Nagaev & Vladimir Chebotarev, 2021. "On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:845-:d:535036
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