Estimates of Proximity to the Normal Distribution in Sampling without Replacement

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Previous article Next article Estimates of Proximity to the Normal Distribution in Sampling without ReplacementSh. A. MirakhmedovSh. A. Mirakhmedovhttps://doi.org/10.1137/1130058PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. I. Ivchenko and , V. V. Levin, Asymptotic normality in the scheme of simple random sampling without replacement, Theory Prob. Appl., 23 (1978), 93–105 0425.62009 LinkGoogle Scholar[2] R. N. Bhattacharya and , R. R. Rao, Normal approximation and asymptotic expansions, John Wiley & Sons, New York-London-Sydney, 1976xiv+274 55:9219 0331.41023 Google Scholar[3] Bengt von Bahr, On sampling from a finite set of independent random variables, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 24 (1972), 279–286 48:9804 0237.62014 CrossrefGoogle Scholar[4] Thomas Höglund, Sampling from a finite population: a remainder term estimate, Scand. J. Statist., 5 (1978), 69–71 57:10868 0382.60028 Google Scholar[5] Sh. A. Mirakhmedov, Estimates for closeness to the normal law of the distribution of a sample sum from a finite population of independent random variablesRandom processes and mathematical statistics (Russian), “Fan”, Tashkent, 1983, 125–137, 238, (In Russian.) 932 508 Google Scholar[6] V. V. Levin, Masters Thesis, Multidimensional limit theorems for divisible statistics and their statistical applications, Dissertation, Faculty of Phys.-Math. Sciences, MIEM, Moscow, 1978, (In Russian.) Google Scholar[7] V. A. Vatutin and , V. G. Mikhailov, Limit theorems for the number of empty cells in an equiprobable scheme for group allocation of particles, Theory Prob. Appl., 27 (1982), 734–743 0536.60017 LinkGoogle Scholar[8] V. G. Mikhailov, Convergencee to the multidimensional normal law in an equiprobable scheme of distributing particles by groups, Math. USSR Sbornik, 39 (1981), 145–167 CrossrefGoogle Scholar[9] V. F. Kolchin, , B. A. Sevast'yanov and , V. P. Chistyakov, Random Allocations, Halstead Press (Wiley), New York, 1978 0376.60003 Google Scholar[10] V. V. Yurinskii, A smoothing inequality for estimates of the Lévy-Prokhorov distance, Theory Prob. Appl., 20 (1975), 1–10 0351.60007 LinkGoogle Scholar[11] G. Englund, A remainder term estimate for the asymptotic normality of order statistics from a finite population, 1982–83, Trita-Mat, May, Mathematical Statistics Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On Edgeworth Expansions in Generalized Urn ModelsJournal of Theoretical Probability, Vol. 27, No. 3 | 17 October 2012 Cross Ref On the Asymptotic Normality of Randomized Separable Statistics in a Generalized Allocation SchemeG. I. Ivchenko and Sh. A. MirakhmedovTheory of Probability & Its Applications, Vol. 33, No. 4 | 28 July 2006AbstractPDF (655 KB)Summary of Reports Presented at Sessions of the Seminar on Probability Theory and Mathematical Statistics at the V. A. Steklov Mathematics Institute of the USSR Academy of Sciences, November 1984–July 1985Theory of Probability & Its Applications, Vol. 31, No. 2 | 3 August 2006AbstractPDF (384 KB) Volume 30, Issue 3| 1986Theory of Probability & Its Applications439-659 History Submitted:07 July 1983Published online:17 July 2006 InformationCopyright © 1986 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130058Article page range:pp. 451-464ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics