Poisson Limit Theorems in an Allocation Scheme with an Even Number of Particles in Each Cell

We consider an allocation scheme of distinguishable particles by different cells under the condition than each cell contains an even number of particles. We show that this scheme is a general allocation scheme defined by the random variable with the distribution . Let be a number of cells from the f...

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Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 41; no. 3; pp. 289 - 297
Main Authors Abdushukurov, F. A., Chuprunov, A. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2020
Springer Nature B.V
Subjects
Algebra
Analysis
Convergence
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Random variables
Gaussian random variable
Berry–Essen type inequality
Poisson random variable
allocation scheme
local limit theorem
Poisson limit theorem
limit theorem
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Summary:We consider an allocation scheme of distinguishable particles by different cells under the condition than each cell contains an even number of particles. We show that this scheme is a general allocation scheme defined by the random variable with the distribution . Let be a number of cells from the first cells that contain particles. We prove that under some types of convergence of to infinity converges in distribution to the Poisson random variable. The limit Poisson random variable is described.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080220030026