On a Refinement of the Central Limit Theorem for Sums of Independent Random Indicators

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Previous article Next article On a Refinement of the Central Limit Theorem for Sums of Independent Random IndicatorsV. G. MikhailovV. G. Mikhailovhttps://doi.org/10.1137/1138044PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractExplicit and rather tight upper bounds for the distance (in the uniform metric) between the distribution function of a sum of independent random indicators and its asymptotic expansion are obtained.[1] V. V. Petrov, Limit Theorems for Sums of Independent Random Variables, Nauka, Moscow, 1987, (In Russian.) Google Scholar[2] V. M. Zolotarev, Real refinements of limit theorems in probability theory, Trudy Mat. Inst. Steklov., 182 (1988), 24–47, (In Russian.) 89k:60038 Google Scholar[3] V. A. Vatutin and , V. G. Mikhailov, Limit theorems for the number of empty cells in equiprobable scheme for group allocation of particles, Theory Probab. Appl., 27 (1982), 734–743 10.1137/1127084 0536.60017 LinkGoogle Scholar[4] Valentin F. Kolchin, , Boris A. Sevastyanov and , Vladimir P. Chistyakov, Random allocations, V. H. Winston & Sons, Washington, D.C., 1978xi+262 57:10758b 0376.60003 Google Scholar[5] V. A. Ivanov, , C. I. Ivchenko and , Yu. I. Medvedev, Discrete problems in probability theory, Soviet Math., 31 (1985), 2– 0579.62001 Google Scholar[6] Paul Deheuvels, , Madan L. Puri and , Stefan S. Ralescu, Asymptotic expansions for sums of nonidentically distributed Bernoulli random variables, J. Multivariate Anal., 28 (1989), 282–303 10.1016/0047-259X(89)90111-5 90k:62039 0676.60024 CrossrefGoogle Scholar[7] William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons Inc., New York, 1966xviii+636 35:1048 0138.10207 Google Scholar[8] S. N. Bernstein, Collected Works, Vol. 4, Nauka, Moscow, 1964, (In Russian.) Google Scholar[9] L. N. Bolshev and , N. V. Smirnov, Tables of Mathematical Statistics, Nauka, Moscow, 1983, (In Russian.) 0529.62099 Google ScholarKeywordsrandom indicatorsnonhomogenuous Bernoulli schemeasymptotic expansioncloseness of approximation Previous article Next article FiguresRelatedReferencesCited byDetails The Chebyshev--Edgeworth Correction in the Central Limit Theorem for Integer-Valued Independent SummandsS. G. Bobkov and V. V. Ulyanov3 February 2022 | Theory of Probability & Its Applications, Vol. 66, No. 4AbstractPDF (426 KB)On the Computation and Approximation of Outage Probability in Satellite Networks With Smart Gateway DiversityIEEE Transactions on Aerospace and Electronic Systems, Vol. 57, No. 1 Cross Ref Поправка Чебышeва-Эджворта в центральной предельной теореме для целочисленных независимых слагаемых22 October 2021 | Теория вероятностей и ее применения, Vol. 66, No. 4 Cross Ref A simple and fast method for computing the Poisson binomial distribution functionComputational Statistics & Data Analysis, Vol. 122 Cross Ref Inferring monopartite projections of bipartite networks: an entropy-based approach17 May 2017 | New Journal of Physics, Vol. 19, No. 5 Cross Ref Sparse covers for sums of indicators2 November 2014 | Probability Theory and Related Fields, Vol. 162, No. 3-4 Cross Ref Learning Poisson Binomial Distributions11 February 2015 | Algorithmica, Vol. 72, No. 1 Cross Ref Asymptotic identifiability of nonparametric item response modelsPsychometrika, Vol. 66, No. 4 Cross Ref Binomial Approximation to the Poisson Binomial Distribution: The Krawtchouk Expansion25 July 2006 | Theory of Probability & Its Applications, Vol. 45, No. 2AbstractPDF (184 KB)A Refinement of the Central Limit Theorem for Sums of Independent Random Indicators12 July 2006 | Theory of Probability & Its Applications, Vol. 40, No. 4AbstractPDF (442 KB) Volume 38, Issue 3| 1994Theory of Probability & Its Applications History Submitted:04 September 1990Published online:17 July 2006 InformationCopyright © 1993 Society for Industrial and Applied MathematicsKeywordsrandom indicatorsnonhomogenuous Bernoulli schemeasymptotic expansioncloseness of approximationPDF Download Article & Publication DataArticle DOI:10.1137/1138044Article page range:pp. 479-489ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics