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Gaussian Limit Theorems for the Number of Given Value Cells in the Non-Homogeneous Generalized Allocation Scheme

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In some non-homogeneous generalized allocation schemes we formulate conditions under which the number of given value cells from the first K cells converges to a Gaussian random variable. This result is applied to the study of the type I error and the type II error for analogs of the empty boxes test.

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References

  1. V. F. Kolchin, “A certain class of limit theorems for conditional distributions,” Litovsk. Math. Sb., 8, No. 1, 53–63 (1968).

    MathSciNet  MATH  Google Scholar 

  2. V.F. Kolchin, Random Graphs, Cambridge University Press (1999).

  3. Yu.L. Pavlov, Random Forests, VSP (2000).

  4. A. N. Timashev, Asymptotic Expansions in Probabilistic Combinatorics, TVP Science Publishers, Moscow (2011).

    Google Scholar 

  5. A. N. Timashev, Generalized Allocation Scheme in Problems of Probabilistic Combinatorics, Akademia Publishing House, Moscow (2011).

    Google Scholar 

  6. E. R. Khakimullin and N. Y. Enatskaya, “Limit theorems for a number of empty cells,” Discr. Math. Appl., 7, No. 2, 209–219 (1997).

    MathSciNet  MATH  Google Scholar 

  7. I. G. Shevtsova, “On the absolute constants in the Berry–Esseen inequality and its structural and nonuniform improvements,” Inform. Primen., 7, No. 1, 124–125 (2013).

    MathSciNet  Google Scholar 

  8. V. Bentkus, “On the asymptotical behavior of the constant in the Berry–Essen inequality,” J. Theor. Prob., 7, No. 2, 211–224 (1994).

    Article  Google Scholar 

  9. A. V. Kolchin and V. F. Kolchin, “On transition of distributions of sums of independent identically distributed random variables from one lattice to another in the generalised allocation scheme,” Discr. Math. Appl., 16, No. 6, 527–540 (2006).

    Article  Google Scholar 

  10. V. F. Kolchin, B. P. Sevast’ynov, and V. P. Chistiakov, Random Allocation, V. H. Winston & Sons, Washington, DC (1978).

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Author information

Authors and Affiliations

  1. Kazan Federal University, Institute of Physics, Department of Radiophysics, Kazan, Russia

    D. E. Chickrin

  2. Almetyevsk State Oil Institute, Almetyevsk, Russia

    A. N. Chuprunov

  3. Kazan Federal University, Institute of Physics, Department of Radiophysics, Kazan, Russia

    P. A. Kokunin

Authors
  1. D. E. Chickrin
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  2. A. N. Chuprunov
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  3. P. A. Kokunin
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Corresponding author

Correspondence to D. E. Chickrin.

Additional information

Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Perm, Russia, September 24–28, 2018. Part I.

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Chickrin, D.E., Chuprunov, A.N. & Kokunin, P.A. Gaussian Limit Theorems for the Number of Given Value Cells in the Non-Homogeneous Generalized Allocation Scheme. J Math Sci 246, 476–487 (2020). https://doi.org/10.1007/s10958-020-04753-w

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  • DOI: https://doi.org/10.1007/s10958-020-04753-w

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