Previous article Next article Superlarge Deviation Probabilities for Sums of Independent Random Variables with Exponentially Decreasing Tails. IIL. V. RozovskyL. V. Rozovskyhttps://doi.org/10.1137/S0040585X97986990PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIn the paper we study large deviation probabilities of a sum of independent identically distributed random variables, whose distribution function has an exponentially decreasing tail at infinity.1. V. V. Petrov , On the probabilities of large deviations for sums of independent random variables , Theory Probab. Appl. , 10 ( 1965 ), pp. 287 -- 298 . LinkGoogle Scholar2. A. A. Borovkov and B. A. Rogozin , On the multi-dimensional central limit theorem , Theory Probab. Appl. , 10 ( 1965 ), pp. 55 -- 62 . LinkGoogle Scholar3. T. Höglund , A unified formulation of the central limit theorem for small and large deviations from the mean , Z. Wahrsch. Verw. Geb. , 49 ( 1979 ), pp. 105 -- 117 . CrossrefGoogle Scholar4. L. V. Rozovsky , On a lower bound for probabilities of large-deviations for a sample mean under the Cramér condition, J. Math. Sci. (N. Y.) , 118 ( 2003 ), pp. 5624 -- 5634 . Google Scholar5. L. V. Rozovsky , Probabilities of large-deviations for some classes of distributions satisfying the Cramér condition, J. Math. Sci. (N. Y.) , 128 ( 2005 ), pp. 2585 -- 2600 . Google Scholar6. H. E. Daniels , Saddlepoint approximations in statistics , Ann. Math. Statist. , 25 ( 1954 ), pp. 631 -- 650 . CrossrefGoogle Scholar7. A. V. Nagaev , Large deviations for one class of distributions, in Limit Theorems in Probability Theory , Tashkent , 1963 , pp. 56 -- 68 (in Russian). Google Scholar8. A. V. Nagaev , Cramér large deviations when the extreme conjugate distribution is heavy-tailed , Theory Probab. Appl. , 43 ( 1999 ), pp. 405 -- 421 . LinkGoogle Scholar9. L. V. Rozovsky , Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cramér condition , Theory Probab. Appl. , 48 ( 2004 ), pp. 108 -- 130 . LinkGoogle Scholar10. A. A. Borovkov and A. A. Mogulskii , On large and superlarge deviations of sums of independent random vectors under Cramér's condition. II , Theory Probab. Appl. , 51 ( 2007 ), pp. 567 -- 594 . LinkGoogle Scholar11. L. V. Rozovsky , Superlarge deviation probabilities for sums of independent random variables with exponential decreasing distributions , Theory Probab. Appl. , 52 ( 2008 ), pp. 167 -- 171 . LinkGoogle Scholar12. L. V. Rozovsky , Superlarge deviation probabilities for sums of independent lattice random variables with exponential decreasing tails , Statist. Probab. Lett. , 82 ( 2012 ), pp. 72 -- 76 . CrossrefGoogle Scholar13. L. V. Rozovsky , Small deviation probabilities for positive random variables, J. Math. Sci. (N. Y.) , 137 ( 2006 ), pp. 4561 -- 4566 . Google Scholar14. V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag, Berlin, New York, 1975.Google ScholarKeywordssums of independent random variablesCramér transformlarge deviationssuperlarge deviations Previous article Next article FiguresRelatedReferencesCited byDetails Small Deviation Probabilities for a Weighted Sum of Independent Positive Random Variables with Common Distribution Function That Can Decrease at Zero Fast EnoughL. V. Rozovsky24 October 2018 | Theory of Probability & Its Applications, Vol. 63, No. 1AbstractPDF (156 KB)Вероятности малых уклонений взвешенной суммы независимых положительных случайных величин, общая функция распределения которых может убывать в нуле достаточно быстроТеория вероятностей и ее применения, Vol. 63, No. 1 Cross Ref Volume 59, Issue 1| 2015Theory of Probability & Its Applications History Submitted:16 March 2012Published online:25 March 2015 Information© 2015, Society for Industrial and Applied MathematicsKeywordssums of independent random variablesCramér transformlarge deviationssuperlarge deviationsPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97986990Article page range:pp. 168-177ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics