Limit Theorems for Number of Particles from a Fixed Set of Cells
- Авторлар: Chuprunov A.1, Kokunin P.2, Chickrin D.2
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Мекемелер:
- N. I. Lobachevskii Institute of Mathematics and Mechanics
- Institute of Physics, Kazan (Volga Region) Federal University
- Шығарылым: Том 40, № 5 (2019)
- Беттер: 624-629
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204411
- DOI: https://doi.org/10.1134/S1995080219050044
- ID: 204411
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
A. Chuprunov
N. I. Lobachevskii Institute of Mathematics and Mechanics
Хат алмасуға жауапты Автор.
Email: achuprunov@mail.ru
Ресей, Kazan, Tatarstan, 420008
P. Kokunin
Institute of Physics, Kazan (Volga Region) Federal University
Хат алмасуға жауапты Автор.
Email: pkokunin@mail.ru
Ресей, Kazan, Tatarstan, 420008
D. Chickrin
Institute of Physics, Kazan (Volga Region) Federal University
Хат алмасуға жауапты Автор.
Email: dmitry.kfu@gmail.com
Ресей, Kazan, Tatarstan, 420008