Previous article Next article On the Asymptotic Normality of Randomized Separable Statistics in a Generalized Allocation SchemeG. I. Ivchenko and Sh. A. MirakhmedovG. I. Ivchenko and Sh. A. Mirakhmedovhttps://doi.org/10.1137/1133117PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. F. Kolchin, , V. A. Sevast'yanov and , V. P. Chistyakov, Random Allocations, Halstead Press, (John Wiley), New York, 1978 0464.60003 Google Scholar[2] Valentin F. Kolchin, Random mappings, Translation Series in Mathematics and Engineering, Optimization Software Inc. Publications Division, New York, 1986xiv + 207 88a:60022 0605.60010 Google Scholar[3] G. I. Ivchenko, A generalized allocation scheme and some realizations of it, Theory Probab. Appl., 31 (1986), 544–545 10.1137/1131077 LinkGoogle Scholar[4] G. I. Ivchenko, Moments of separable statistics in a generalized allocation scheme, Mat. Zametki, 39 (1986), 284–294, 303, (In Russian.) 87h:60028 Google Scholar[5] Yu. I. Medvedev, Some theorems on the asymptotic distribution of a $\chi^2$ statistic, Soviet Math. Dokl., 11 (1970), 770–773 0212.22803 Google Scholar[6] V. A. Ivanov and , S. A. Lapin, Asymptotic normality of randomized decomposable statistics in a multinomial scheme, Mat. Zametki, 34 (1983), 745–756, (In Russian.) 85f:60038 0536.62007 Google Scholar[7] V. A. Ivanov, , G. I. Ivchenko and , Yu. I. Medvedev, Discrete problems in probability theoryProbability theory. Mathematical statistics. Theoretical cybernetics, Vol. 22, Itogi Nauki i Tekhniki, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984, 3–60, 204, (In Russian.) 86g:60029 Google Scholar[8] Sh. A. Mirakhmedov, Estimates of closeness of the distribution of a randomized separable statistic to the normal law in a multinomial scheme, Theory Probab. Appl., 30 (1985), 192–196 10.1137/1130025 0658.62015 LinkGoogle Scholar[9] Sh. A. Mirakhmedov, Estimates of proximity to the normal law in sampling without replacement, Theory Probab. Appl., 30 (1985), 451–464 10.1137/1130058 0594.60033 LinkGoogle Scholar[10] G. I. Ivchenko and , Yu. I. Medvedev, Estimation of the rate of convergence in limit theorems for separable statistics, Theory Probab. Appl., 31 (1986), 81–87 10.1137/1131007 0602.60029 LinkGoogle Scholar[11] G. I. Ivchenko, , Yu. I. Medvedev and , A. F. Ronzhin, Decomposable statistics and goodness-of-fit tests for multinomial samples, Trudy Mat. Inst. Steklov., 177 (1986), 60–74, 207, (In Russian.) 87i:62087 Google Scholar[12] V. A. Ivanov, Randomized decomposable statistics, Trudy Mat. Inst. Steklov., 177 (1986), 47–59, 207, (In Russian.) 88m:62030 Google Scholar[13] A. N. Trunov, Limit theorems in the problem of allocation of identical particles among different cells, Trudy Mat. Inst. Steklov., 177 (1986), 147–164, 208–209, (In Russian.) 87k:60035 Google Scholar[14] M. P. Quine and , J. Robinson, Normal approximations to sums of scores based on occupancy numbers, Ann. Probab., 12 (1984), 794–804 85h:60035 0584.60031 CrossrefGoogle Scholar[15] Yu. V. Prokhorov, On a local limit theorem for lattice distributions, Dokl. Akad. Nauk SSSR (N.S.), 98 (1954), 535–538, (In Russian.) 16,494c Google Scholar[16] Yu. A. Rozanov, On a local limit theorem for lattice distributions, Theory Probab. Appl., 2 (1957), 260–265 10.1137/1102018 LinkGoogle Scholar[17] A. B. Mukhin, Local limit theorems for an arbitrary law. I, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1977), 24–27, 97, (In Russian.) 56:1415 A. B. Mukhin, Local limit theorems for an arbitrary law. II, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1977), 18–22, 84, (In Russian.) 56:13323 A. B. Mukhin, Local limit theorems for an arbitrary law. III, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1978), 30–36, 86, (In Russian.) 58:13284 Google Scholar[18] Vo An Zung, , A. B. Mukhin and , To An Zung, Certain local limit theorems for independent integer-valued random variables, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1980), 9–15, 99, (In Russian.) 82d:60046 0494.60028 Google Scholar[19] R. N. Bhattacharya and , R. Ranga Rao, Normal approximation and asymptotic expansions, John Wiley & Sons, New York-London-Sydney, 1976xiv+274 55:9219 0331.41023 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Some Examples of Normal Approximations by Stein’s Method Cross Ref Volume 33, Issue 4| 1989Theory of Probability & Its Applications History Submitted:10 November 1986Published online:28 July 2006 InformationCopyright © 1988 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1133117Article page range:pp. 749-755ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics