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Refinements of Yu. V. Prokhorov's theorems on the asymptotic behavior of the binomial distribution

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Abstract

One finds the asymptotic behavior of the minimax distance between the binomial and its approximating normal or Poisson “distributions,” taken with the second terms of their expansions.

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Literature cited

  1. Yu. V. Prokhorov, “The asymptotic behavior of the binomial distribution,” Usp. Mat. Nauk,8 No. 3, 135–142 (1953).

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  2. B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading (1954).

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  3. S. N. Bernshtein, Theory of Probability [in Russian], Gostekhizdat, Moscow (1946).

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Authors
  1. T. A. Azlarov
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  2. T. L. Gurvich
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Additional information

Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 4–19, 1986.

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Azlarov, T.A., Gurvich, T.L. Refinements of Yu. V. Prokhorov's theorems on the asymptotic behavior of the binomial distribution. J Math Sci 38, 2161–2170 (1987). https://doi.org/10.1007/BF01093817

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  • DOI: https://doi.org/10.1007/BF01093817

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