Approximation in Variation of the Distribution of a Sum of Independent Bernoulli Variables with a Poisson Law

Abstract

Previous article Next article Approximation in Variation of the Distribution of a Sum of Independent Bernoulli Variables with a Poisson LawE. L. PresmanE. L. Presmanhttps://doi.org/10.1137/1130051PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Lucien Le Cam, An approximation theorem for the Poisson binomial distribution, Pacific J. Math., 10 (1960), 1181–1197 25:5567 0118.33601 CrossrefGoogle Scholar[2] S. Ya. Shorgin, Approximation of a generalized binomial distribution, Theory Prob. Appl., 22 (1977), 846–850 0392.60021 LinkGoogle Scholar[3] Yu. V. Prokhorov, The asymptotic behavior of a binomial distribution, Uspekhi Matem. Nauk., 8 (1956), 135–142, (In Russian.) Google Scholar[4] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– 48:1287 0219.60027 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Asymptotics for the sum of three state Markov dependent random variables19 November 2018 | Modern Stochastics: Theory and Applications, Vol. 19 Cross Ref Poisson approximationProbability Surveys, Vol. 16, No. none Cross Ref Toward the History of the Saint Petersburg School of Probability and Statistics. I. Limit Theorems for Sums of Independent Random Variables16 June 2018 | Vestnik St. Petersburg University, Mathematics, Vol. 51, No. 2 Cross Ref A study of bias and increasing organismal complexity from their post-translational modifications and reaction site interplays13 January 2016 | Briefings in Bioinformatics, Vol. 18, No. 1 Cross Ref Definitions and Preliminary Facts17 June 2016 Cross Ref Heinrich’s Method for m-Dependent Variables17 June 2016 Cross Ref Other Methods17 June 2016 Cross Ref The Method of Convolutions17 June 2016 Cross Ref Local Lattice Estimates17 June 2016 Cross Ref Uniform Lattice Estimates17 June 2016 Cross Ref Total Variation of Lattice Measures17 June 2016 Cross Ref A Compound Poisson Convergence Theorem for Sums of $$m$$ m -Dependent Variables31 January 2014 | Journal of Theoretical Probability, Vol. 28, No. 3 Cross Ref Two limit theorems for Markov binomial distribution7 August 2015 | Lithuanian Mathematical Journal, Vol. 55, No. 3 Cross Ref Compound Poisson approximation to weighted sums of symmetric discrete variables23 January 2014 | Annals of the Institute of Statistical Mathematics, Vol. 67, No. 1 Cross Ref Smoothing effect of compound Poisson approximations to the distributions of weighted sums11 March 2014 | Lithuanian Mathematical Journal, Vol. 54, No. 1 Cross Ref Compound poisson approximations for sums of 1-dependent random variables. II15 March 2011 | Lithuanian Mathematical Journal, Vol. 51, No. 1 Cross Ref Compound Poisson approximations for sums of 1-dependent random variables. I26 August 2010 | Lithuanian Mathematical Journal, Vol. 50, No. 3 Cross Ref An expansion in the exponent for compound binomial approximationsLithuanian Mathematical Journal, Vol. 46, No. 1 Cross Ref Lower-Bound Estimates for Poisson-Type ApproximationsLithuanian Mathematical Journal, Vol. 45, No. 4 Cross Ref Rate of Convergence to Poisson Law in Terms of Information DivergenceIEEE Transactions on Information Theory, Vol. 50, No. 9 Cross Ref Binomial and Poisson distributions as maximum entropy distributionsIEEE Transactions on Information Theory, Vol. 47, No. 5 Cross Ref On Compound Poisson Approximations Under Moment RestrictionsV. Cekanavicius25 July 2006 | Theory of Probability & Its Applications, Vol. 44, No. 1AbstractPDF (147 KB)Signed Poisson approximations for Markov chainsStochastic Processes and their Applications, Vol. 82, No. 2 Cross Ref Metric Multivariate Poisson Approximation of the Generalized Multinomial DistributionB. Roos25 July 2006 | Theory of Probability & Its Applications, Vol. 43, No. 2AbstractPDF (357 KB)On a centered Poisson approximationLithuanian Mathematical Journal, Vol. 38, No. 4 Cross Ref Poisson approximations for sequences of random variablesStatistics & Probability Letters, Vol. 39, No. 2 Cross Ref Asymptotic expansions for compound Poisson measuresLithuanian Mathematical Journal, Vol. 37, No. 4 Cross Ref Approximation of the generalized Poisson binomial distribution: Asymptotic expansionsLithuanian Mathematical Journal, Vol. 37, No. 1 Cross Ref Convergence of Probability Measures. Central Limit Theorem Cross Ref Le Cam's Inequality and Poisson Approximations18 April 2018 | The American Mathematical Monthly, Vol. 101, No. 1 Cross Ref Volume 30, Issue 2| 1986Theory of Probability & Its Applications History Published online:17 July 2006 InformationCopyright © 1986 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130051Article page range:pp. 417-422ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics