This article is cited in 6 scientific papers (total in 6 papers)
Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications
Abstract:
The properties of the distribution of the number of empty cells are analyzed for a natural generalization of an equiprobable scheme for group allocation of particles. An error estimate is obtained for the Chen–Stein method of Poisson approximation for the distribution of the number of empty cells in this scheme. This estimate is used to derive sufficient conditions for the distribution of the number of empty cells to converge to the convolutions of the Poisson distribution and two-point distributions. On the basis of these results, asymptotic properties of the solution set of a perturbed system of linear Boolean equations are studied (in the case of consistent increase in the number of unknowns and the number of equations).
Citation:
V. G. Mikhailov, “Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 165–180; Proc. Steklov Inst. Math., 282 (2013), 157–171
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\paper Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications
\inbook Branching processes, random walks, and related problems
\bookinfo Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2013
\vol 282
\pages 165--180
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
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\vol 282
\pages 157--171
\crossref{https://doi.org/10.1134/S008154381306014X}
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https://www.mathnet.ru/eng/tm/v282/p165
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