Nonuniform Estimates of the Accuracy of Normal Approximation of the Distributions of Random Sums of Independent Random Variables
Victor Yu. Korolev · Theory of Probability and Its Applications · 1989
Previous article Next article Nonuniform Estimates of the Accuracy of Normal Approximation of the Distributions of Random Sums of Independent Random VariablesV. Yu. KorolevV. Yu. Korolevhttps://doi.org/10.1137/1133118PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. Yu. Korolev, On the accuracy of normal approximation of distributions of random sums of independent random variables, Theory Probab. Appl., 33 (1988), 540–543 10.1137/1133079 0676.60045 LinkGoogle Scholar[2] S. Kh. Sirazhdinov, , M. Mamatov and , Sh. K. Formanov, Uniform estimates in limit theorems for sums of a random number of independent random variables, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, 14 (1970), 28–34, (In Russian.) 44:1090 Google Scholar[3] A. Bikyalis, Estimates of the remainder term in the central limit theorem, Litovsk. Mat. Sb., 6 (1966), 323–346, (In Russian.) 35:1067 Google Scholar[4] Sh. A. Mirakhmedov, On the absolute constant in a nonuniform estimate of the rate of convergence in the central limit theorem, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1984), 26–30, 78, (In Russian.) 86i:60071 0557.60017 Google Scholar[5] S. V. Nagaev, Some limit theorems for large deviations, Theory Probab. Appl., 10 (1965), 214–235 10.1137/1110027 LinkGoogle Scholar[6] V. I. Paulauskas, The sum of a random number of multidimensional random vectors, Litovsk. Mat. Sb., 12 (1972), 109–131, 205, (In Russian.) 47:5928 Google Scholar[7] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346, Berlin 52:9335 0322.60042 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Nonuniform estimates of the stability of the normal law under random perturbations of the scale parameter and some of their applicationsJournal of Soviet Mathematics, Vol. 57, No. 4 Cross Ref Approximation of Distributions of Random Sums of Independent Random Variables by Mixtures of Normal LawsV. Yu. Korolev17 July 2006 | Theory of Probability & Its Applications, Vol. 34, No. 3AbstractPDF (934 KB)The asymptotic distributions of random sums29 September 2006 Cross Ref Volume 33, Issue 4| 1989Theory of Probability & Its Applications History Submitted:30 April 1986Published online:28 July 2006 InformationCopyright © 1988 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1133118Article page range:pp. 755-759ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics