Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 328-338
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L. V. Osipov. On asymptotic expansions for distribution functions of sums of independent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 328-338. http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a9/
@article{TVP_1971_16_2_a9,
author = {L. V. Osipov},
title = {On asymptotic expansions for distribution functions of sums of independent random variables},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {328--338},
year = {1971},
volume = {16},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a9/}
}
TY - JOUR
AU - L. V. Osipov
TI - On asymptotic expansions for distribution functions of sums of independent random variables
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1971
SP - 328
EP - 338
VL - 16
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a9/
LA - ru
ID - TVP_1971_16_2_a9
ER -
%0 Journal Article
%A L. V. Osipov
%T On asymptotic expansions for distribution functions of sums of independent random variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
%P 328-338
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a9/
%G ru
%F TVP_1971_16_2_a9
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).
