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Teor. Veroyatnost. i Primenen., 1971, Volume 16, Issue 2, Pages 328–338 (Mi tvp2152)  

On asymptotic expansions for distribution functions of sums of independent random variables

L. V. Osipov

Leningrad

Abstract: Let $\{X_j\}$ be a sequence of independent identically distributed random variables with zero means and unit variances and let $F_n(x)$ be the distribution function of the sum $\frac1{\sqrt n}\sum_{j=1}^nX_j$. Asymptotic expansions of the function $F_n(x)$ are given which are more general than the classic expansion (0.1). We study also the asymptotic behaviour of the remainder in (0.1).

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English version:
Theory of Probability and its Applications, 1971, 16:2, 333–343

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Citation: L. V. Osipov, “On asymptotic expansions for distribution functions of sums of independent random variables”, Teor. Veroyatnost. i Primenen., 16:2 (1971), 328–338; Theory Probab. Appl., 16:2 (1971), 333–343

Citation in format AMSBIB
\Bibitem{Osi71}
\by L.~V.~Osipov
\paper On asymptotic expansions for distribution functions of sums of independent random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1971
\vol 16
\issue 2
\pages 328--338
\mathnet{http://mi.mathnet.ru/tvp2152}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=283855}
\zmath{https://zbmath.org/?q=an:0248.60015}
\transl
\jour Theory Probab. Appl.
\yr 1971
\vol 16
\issue 2
\pages 333--343
\crossref{https://doi.org/10.1137/1116030}


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