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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 1, Pages 8–22 (Mi smj1819)  
This article is cited in 14 scientific papers (total in 14 papers)

Accuracy of approximation in the Poisson theorem in terms of the $\chi^2$-distance

I. S. Borisova, I. S. Vorozheikinb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
Full-text PDF (327 kB) Citations (14)
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Abstract: We study the limit behavior of the $\chi^2$-distance between the distributions of the $n$th partial sum of independent not necessarily identically distributed Bernoulli random variables and the accompanying Poisson law. As a consequence in the i.i.d. case we make the multiplicative constant preciser in the available upper bound for the rate of convergence in the Poisson limit theorem.
Keywords: generalized binomial distribution, binomial distribution, Poisson distribution, Poisson theorem, Kulback–Leibler distance, total variation distance, $\chi^2$-distance.
Received: 18.06.2006
Revised: 25.07.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 1, Pages 5–17
DOI: https://doi.org/10.1007/s11202-008-0002-3
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: I. S. Borisov, I. S. Vorozheikin, “Accuracy of approximation in the Poisson theorem in terms of the $\chi^2$-distance”, Sibirsk. Mat. Zh., 49:1 (2008), 8–22; Siberian Math. J., 49:1 (2008), 5–17
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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