Limit Theorems for Number of Particles from a Fixed Set of Cells
- 作者: Chuprunov A.1, Kokunin P.2, Chickrin D.2
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隶属关系:
- N. I. Lobachevskii Institute of Mathematics and Mechanics
- Institute of Physics, Kazan (Volga Region) Federal University
- 期: 卷 40, 编号 5 (2019)
- 页面: 624-629
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204411
- DOI: https://doi.org/10.1134/S1995080219050044
- ID: 204411
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详细
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.
作者简介
A. Chuprunov
N. I. Lobachevskii Institute of Mathematics and Mechanics
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Email: achuprunov@mail.ru
俄罗斯联邦, Kazan, Tatarstan, 420008
P. Kokunin
Institute of Physics, Kazan (Volga Region) Federal University
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Email: pkokunin@mail.ru
俄罗斯联邦, Kazan, Tatarstan, 420008
D. Chickrin
Institute of Physics, Kazan (Volga Region) Federal University
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Email: dmitry.kfu@gmail.com
俄罗斯联邦, Kazan, Tatarstan, 420008