On the Closeness of the Distributions of Two Sums of Independent Random Variables
Vladimir Mikhailovich Zolotarev · Theory of Probability and Its Applications · 1965
Previous article Next article On the Closeness of the Distributions of Two Sums of Independent Random VariablesV. M. ZolotarevV. M. Zolotarevhttps://doi.org/10.1137/1110055PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Andrew C. Berry, The accuracy of the Gaussian approximation to the sum of independent variates, Trans. Amer. Math. Soc., 49 (1941), 122–136 MR0003498 0025.34603 CrossrefGoogle Scholar[2] V. M. Zolotarev, Analogue of the asymptotic Edgeworth-Cramer expansion in the case of convergence to stable distributions, Proc. Sixth All-Union Conf. Theory Prob. and Math. Statist. (Vilnius, 19 60) (Russian), Gosudarstv. Izdat. Političesk. i Naučn. Lit. Litovsk. SSR, Vilnius, 1962, 49–50, (In Russian.) MR0190986 Google Scholar[3] V. M. Zolotarev, One-sided interpretation and revision of certain inequalities ofthe Čbyšev type, Litovsk. Mat. Sb., 5 (1965), 233–250, (In Russian.) MR0195131 Google Scholar[4] I. P. Tsaregradskii, On uniform approximation of the binomial distribution by infinitely divisible laws, Theory Prob. Applications, 3 (1958), 434–438, (English translation.) 10.1137/1103038 0100.14101 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The method of cumulants for the normal approximationProbability Surveys, Vol. 19, No. none | 1 Jan 2022 Cross Ref Nonclassical Berry–Esseen inequalities and accuracy of the bootstrapThe Annals of Statistics, Vol. 48, No. 4 | 1 Aug 2020 Cross Ref Moment-Type Estimates for Characteristic Functions with Application to Von Mises Inequality*Journal of Mathematical Sciences, Vol. 214, No. 1 | 20 February 2016 Cross Ref On the accuracy of the approximation of the complex exponent by the first terms of its Taylor expansion with applicationsJournal of Mathematical Analysis and Applications, Vol. 418, No. 1 | 1 Oct 2014 Cross Ref An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sumsScandinavian Actuarial Journal, Vol. 2012, No. 2 | 1 Jun 2012 Cross Ref On the Convergence Rate in Lyapunov's TheoremI. 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