Previous article Next article On the Normal Approximation to Symmetric Binomial DistributionsC. Hipp and L. MattnerC. Hipp and L. Mattnerhttps://doi.org/10.1137/S0040585X97983213PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe optimal constant over the square root of n error bound in the central limit theorem for distribution functions of sums of independent symmetric Bernoulli random variables is $1/\sqrt{2\pi n}$.[1] J. Bretagnolle and and P. Massart, Hungarian constructions from the nonasymptotic viewpoint, Ann. Probab., 17 (1989), pp. 239–256. APBYAE 0091-1798 CrossrefGoogle Scholar[2] C. G. Esseen, A moment inequality with an application to the central limit theorem, Skand. Aktuarietidskr., 39 (1956), pp. 160–170. Google Scholar[3] C. J. Everett, Inequalities for the Wallis product, Math. Mag., 43 (1970), pp. 30–33. MAMGA8 0025-570X CrossrefGoogle Scholar[4] P. Massart, Tusnady's lemma $24$ years later, Ann. Inst. H. Poincaré, 38 (2002), pp. 991–1007. CrossrefGoogle ScholarKeywordsbinomial distributioncentral limit theoremoptimal error boundsymmetric Bernoulli variables Previous article Next article FiguresRelatedReferencesCited byDetails Guessing about Guessing: Practical Strategies for Card Guessing with Feedback23 May 2022 | The American Mathematical Monthly, Vol. 129, No. 7 Cross Ref A New Test for Hamming-Weight DependenciesACM Transactions on Modeling and Computer Simulation, Vol. 32, No. 3 Cross Ref On normal approximations to symmetric hypergeometric laws7 September 2017 | Transactions of the American Mathematical Society, Vol. 370, No. 1 Cross Ref Sample size calculations for skewed distributions2 April 2015 | BMC Medical Research Methodology, Vol. 15, No. 1 Cross Ref Moment-Type Estimates with an Improved Structure for the Accuracy of the Normal Approximation to Distributions of Sums of Independent Symmetric Random VariablesI. G. Shevtsova4 September 2013 | Theory of Probability & Its Applications, Vol. 57, No. 3AbstractPDF (341 KB)On the accuracy of the normal approximation for sums of symmetric independent random variables5 May 2012 | Doklady Mathematics, Vol. 85, No. 2 Cross Ref On the Bound of Proximity of the Binomial Distribution to the Normal OneS. V. Nagaev and V. I. Chebotarev22 May 2012 | Theory of Probability & Its Applications, Vol. 56, No. 2AbstractPDF (289 KB)On the Upper Bound for the Absolute Constant in the Berry–Esseen InequalityV. Yu. Korolev and I. G. Shevtsova11 November 2010 | Theory of Probability & Its Applications, Vol. 54, No. 4AbstractPDF (259 KB)The Kolmogorov Distance between the Binomial and Poisson Laws: Efficient Algorithms and Sharp EstimatesJournal of Inequalities and Applications, Vol. 2009, No. 1 Cross Ref Volume 52, Issue 3| 2008Theory of Probability & Its Applications History Submitted:04 April 2006Published online:27 August 2008 InformationCopyright © 2008 Society for Industrial and Applied MathematicsKeywordsbinomial distributioncentral limit theoremoptimal error boundsymmetric Bernoulli variablesPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97983213Article page range:pp. 516-523ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics