On the Accuracy of Approximation of Distributions of Sums of Independent Random Variables—Which are Nonzero with a Small Probability—By Means of Accompanying Laws
A. Yu. Zaîtsev · Theory of Probability and Its Applications · 1984
Next article On the Accuracy of Approximation of Distributions of Sums of Independent Random Variables—Which are Nonzero with a Small Probability—By Means of Accompanying LawsA. Yu. ZaitsevA. Yu. Zaitsevhttps://doi.org/10.1137/1128065PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] L. Le Cam, On the distribution of sums of independent random variablesProc. Internat. Res. Sem., Statist. Lab., Univ. California, Berkeley, Calif., Springer-Verlag, New York, 1965, 179–202, Bernoulli, Bayes, Laplace (anniversary volume) 33:8011 Google Scholar[2] Yu. V. Prokhorov, Asymptotic behavior of the binomial distribution, Uspehi Matem. Nauk (N.S.), 8 (1953), 135–142, (In Russian.) 15,138g Google Scholar[3] S. Ya. Shorgin, Approximation of a generalized binomial distribution, Theory Prob. Appl., 22 (1977), 846–850 LinkGoogle Scholar[4] A. Yu. Zaitsev, Masters Thesis, Estimates of the accuracy of approximation of distributions of sums of independent random vectors by infinitely divisible distributions, candidate's thesis, LOMI AN SSSR, Leningrad, 1980, (In Russian.) Google Scholar[5] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Translated from the Russian, annotated, and revised by K. L. Chung. With appendices by J. L. Doob and P. L. Hsu. Revised edition, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills., Ont., 1968ix+293 38:1722 Google Scholar[6] A. N. Kolmogorov, Two uniform limit theorems for sums of independent random variables, Theory Prob. Appl., 1 (1956), 384–394 LinkGoogle Scholar[7] A. N. Kolmogorov, On approximating distributions of sums of independent random variables by infinitely divisible distributions, Tr. Mosk. Matem. Ob-va, 12 (1963), 437–451, (In Russian.) Google Scholar[8] I. A. Ibragimov and , E. L. 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Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346 52:9335 CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails On Alternative Approximating Distributions in the Multivariate Version of Kolmogorov's Second Uniform Limit TheoremF. Götze and A. Yu. ZaitsevTheory of Probability & Its Applications, Vol. 67, No. 1 | 5 May 2022AbstractPDF (451 KB)Compound Poisson approximationProbability Surveys, Vol. 19, No. none | 1 Jan 2022 Cross Ref Об альтернативных аппроксимирующих распределениях в многомерном варианте второй равномерной предельной теоремы КолмогороваТеория вероятностей и ее применения, Vol. 67, No. 1 | 21 January 2022 Cross Ref On the accuracy of Poisson approximationExtremes, Vol. 22, No. 4 | 18 June 2019 Cross Ref Poisson approximationProbability Surveys, Vol. 16, No. none | 1 Jan 2019 Cross Ref Toward the History of the Saint Petersburg School of Probability and Statistics. I. 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