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Limit Theorems for Number of Particles from a Fixed Set of Cells

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Abstract

We conceder random variables that are numbers of particles in the first K cells in a non-homogeneous allocation scheme of distinguishing particles by different cells, where K is a fixed number. It proved that under some conditions the sum of square of centered and normalized these random variables converge in distribution to a χ2-square random variable with K degrees of freedom, sums of these random variables which centered and normalized converge in distribution to a Gaussian random variable with the means 0 and the variance 1. The meathod of the proofs of our theorems founded on Kolchin representation of an allocation scheme of distinguishing particles by different cells. We give applications of these results to mathematical statistics: we consider analog of χ2-test and some S-criterion.

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Authors and Affiliations

  1. Institute of Physics, Kazan (Volga Region) Federal University, Kazan, Tatarstan, 420008, Russia

    D. E. Chickrin & P. A. Kokunin

  2. N. I. Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan, Tatarstan, 420008, Russia

    A. N. Chuprunov

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 authors

Correspondence to D. E. Chickrin, A. N. Chuprunov or P. A. Kokunin.

Additional information

(Submitted by A. I. Volodin)

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Chickrin, D.E., Chuprunov, A.N. & Kokunin, P.A. Limit Theorems for Number of Particles from a Fixed Set of Cells. Lobachevskii J Math 40, 624–629 (2019). https://doi.org/10.1134/S1995080219050044

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  • DOI: https://doi.org/10.1134/S1995080219050044

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