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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| Published in | Lobachevskii journal of mathematics Vol. 41; no. 3; pp. 289 - 297 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.03.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Chuprunov, A. N. Abdushukurov, F. A. |
| Author_xml | – sequence: 1 givenname: F. A. surname: Abdushukurov fullname: Abdushukurov, F. A. email: fayz.abdushukurov@mail.ru organization: Kazan Federal University – sequence: 2 givenname: A. N. surname: Chuprunov fullname: Chuprunov, A. N. email: achuprunov@mail.ru organization: Kazan Federal University |
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| Keywords | Gaussian random variable Berry–Essen type inequality Poisson random variable allocation scheme local limit theorem Poisson limit theorem limit theorem |
| Language | English |
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| References | KolchinV. F.A certain class of limit theorems for conditional distributionsLitovsk. Mat. Sb.1968853632408560235.60023 KolchinA. V.KolchinV. F.On transition of distributions of sums of independent identically distributed random variables from one lattice to another in the generalised allocation schemeDiscrete Math. Appl.200616527540231009710.1515/156939206779218023 KendallD. G.On finite and infinite sequences of exchangeble eventsStudia Sci. Math. Hungar.196723193272215650157.25601 ChuprunovA.FazekasI.“Poisson limit theorems for the for the generalized allocation scheme,” Ann. Univ. Sci. BudapestSect. Comp.201949779607119779 BenczúrA.On sequences of equivalent events and the compound Poisson ProcessStudia Sci. Math. Hungar.196834514582435840279.60038 V. F. Kolchin, B. P. Sevast’ynov, and V. P. Chistiakov, Random Allocation, Scripta Series in Mathematics (V. H. Winston and Sons, Washington, DC, 1978). 6033_CR1 D. G. Kendall (6033_CR3) 1967; 2 A. V. Kolchin (6033_CR6) 2006; 16 A. Benczúr (6033_CR5) 1968; 3 V. F. Kolchin (6033_CR2) 1968; 8 A. Chuprunov (6033_CR4) 2019; 49 |
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| Snippet | We consider an allocation scheme of
distinguishable particles by
different cells under the condition than each cell contains an even number of particles. We... We consider an allocation scheme of distinguishable particles by different cells under the condition than each cell contains an even number of particles. We... |
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| SubjectTerms | Algebra Analysis Convergence Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Random variables |
| Title | Poisson Limit Theorems in an Allocation Scheme with an Even Number of Particles in Each Cell |
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