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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 4, Pages 913–935 (Mi smj2247)  
This article is cited in 5 scientific papers (total in 5 papers)

On the real accuracy of approximation in the central limit theorem

V. V. Senatov

Moscow State University, Moscow, Russia
Full-text PDF (374 kB) Citations (5)
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Abstract: We consider various approximations in the central limit theorem for distributions of sums of independent random variables. We study how many summands in the normalized sums guarantee the precision 10−310−3 for these approximations. It turns out that for the same distribution but different approximations this number varies from hundreds of thousands to a few tens.
Keywords: central limit theorem, accuracy of approximation, asymptotic expansions.
Received: 06.01.2011
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 4, Pages 727–746
DOI: https://doi.org/10.1134/S003744661104015X
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: V. V. Senatov, “On the real accuracy of approximation in the central limit theorem”, Sibirsk. Mat. Zh., 52:4 (2011), 913–935; Siberian Math. J., 52:4 (2011), 727–746
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/smj/v52/i4/p913
    Cycle of papers
    This publication is cited in the following 5 articles:
    1. Alexis Derumigny, Lucas Girard, Yannick Guyonvarch, “Explicit Non-Asymptotic Bounds for the Distance to the First-Order Edgeworth Expansion”, Sankhya A, 86:1 (2024), 261  crossref
    2. V. I. Piterbarg, Yu. A. Shcherbakova, “On accompanying measures and asymptotic expansions in the B. V. Gnedenko limit theorem”, Theory Probab. Appl., 67:1 (2022), 44–61  mathnet  crossref  crossref  mathscinet  zmath
    3. V. V. Senatov, “On the real accuracy of approximation in the central limit theorem. II”, Siberian Adv. Math., 27:2 (2017), 133–152  mathnet  crossref  crossref  elib
    4. A. A. Zaikin, “Defect of the size of nonrandomized test and randomization effect on the necessary sample size in testing the Bernoulli success probability”, Theory Probab. Appl., 59:3 (2015), 466–480  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. Emanuele Dolera, “Estimates of the approximation of weighted sums of conditionally independent random variables by the normal law”, J Inequal Appl, 2013:1 (2013)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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    Full-text PDF :149
    References:58
    First page:11
     
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