Limit Theorems for Number of Particles from a Fixed Set of Cells
- Authors: Chuprunov A.N.1, Kokunin P.A.2, Chickrin D.E.2
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Affiliations:
- N. I. Lobachevskii Institute of Mathematics and Mechanics
- Institute of Physics, Kazan (Volga Region) Federal University
- Issue: Vol 40, No 5 (2019)
- Pages: 624-629
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204411
- DOI: https://doi.org/10.1134/S1995080219050044
- ID: 204411
Cite item
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.
About the authors
A. N. Chuprunov
N. I. Lobachevskii Institute of Mathematics and Mechanics
Author for correspondence.
Email: achuprunov@mail.ru
Russian Federation, Kazan, Tatarstan, 420008
P. A. Kokunin
Institute of Physics, Kazan (Volga Region) Federal University
Author for correspondence.
Email: pkokunin@mail.ru
Russian Federation, Kazan, Tatarstan, 420008
D. E. Chickrin
Institute of Physics, Kazan (Volga Region) Federal University
Author for correspondence.
Email: dmitry.kfu@gmail.com
Russian Federation, Kazan, Tatarstan, 420008