KFU. Card publication. Limit Theorems for Number of Particles from a Fixed Set of Cells

KAZAN
FEDERAL UNIVERSITY

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LIMIT THEOREMS FOR NUMBER OF PARTICLES FROM A FIXED SET OF CELLS

Form of presentation

Articles in international journals and collections

Year of publication

2019

Язык

английский

Authors, employees of KFU

Kokunin Petr Anatolevich, author

Chikrin Dmitriy Evgenevich, author

Chuprunov Aleksey Nikolaevich, author

Bibliographic description in the original language

Limit Theorems for Number of Particles from a Fixed Set of Cells / Chickrin D.E, Chuprunov A.N, Kokunin P.A. // Lobachevskii Journal of Mathematics. 2019. Vol.40, Is.5. P.624-629.

Annotation

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.

Keywords

allocation scheme of distinguishing particles by different cells, χ2-test, S-criterion, type I error, type II error, means unbiased estimator, consistent estimator

The name of the journal

Lobachevskii Journal of Mathematics

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85067869791&doi=10.1134%2fS1995080219050044&partnerID=40&md5=f04826a4eee578359ec84fc44e116855

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=205725&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Kokunin Petr Anatolevich	ru_RU
dc.contributor.author	Chikrin Dmitriy Evgenevich	ru_RU
dc.contributor.author	Chuprunov Aleksey Nikolaevich	ru_RU
dc.date.accessioned	2019-01-01T00:00:00Z	ru_RU
dc.date.available	2019-01-01T00:00:00Z	ru_RU
dc.date.issued	2019	ru_RU
dc.identifier.citation	Limit Theorems for Number of Particles from a Fixed Set of Cells / Chickrin D.E, Chuprunov A.N, Kokunin P.A. // Lobachevskii Journal of Mathematics. 2019. Vol.40, Is.5. P.624-629.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=205725&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.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.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	allocation scheme of distinguishing particles by different cells	ru_RU
dc.subject	χ2-test	ru_RU
dc.subject	S-criterion	ru_RU
dc.subject	type I error	ru_RU
dc.subject	type II error	ru_RU
dc.subject	means unbiased estimator	ru_RU
dc.subject	consistent estimator	ru_RU
dc.title	Limit Theorems for Number of Particles from a Fixed Set of Cells	ru_RU
dc.type	Articles in international journals and collections	ru_RU