On estimation of the remainder in the central limit theorem for sums of functions of independent random variables and sums of the form $\Sigma f(t2^k)$
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 1, pp. 108-116
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V. I. Ladohin; D. A. Moskvin. On estimation of the remainder in the central limit theorem for sums of functions of independent random variables and sums of the form $\Sigma f(t2^k)$. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 1, pp. 108-116. http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a7/
@article{TVP_1971_16_1_a7,
author = {V. I. Ladohin and D. A. Moskvin},
title = {On estimation of the remainder in the central limit theorem for sums of functions of independent random variables and sums of the form $\Sigma f(t2^k)$},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {108--116},
year = {1971},
volume = {16},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a7/}
}
TY - JOUR
AU - V. I. Ladohin
AU - D. A. Moskvin
TI - On estimation of the remainder in the central limit theorem for sums of functions of independent random variables and sums of the form $\Sigma f(t2^k)$
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1971
SP - 108
EP - 116
VL - 16
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a7/
LA - ru
ID - TVP_1971_16_1_a7
ER -
%0 Journal Article
%A V. I. Ladohin
%A D. A. Moskvin
%T On estimation of the remainder in the central limit theorem for sums of functions of independent random variables and sums of the form $\Sigma f(t2^k)$
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
%P 108-116
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a7/
%G ru
%F TVP_1971_16_1_a7
The result of [2] is generalized to the case of sums of functions of independent identically distributed random variables. The dependence of the remainder on $x$ in the theorem of [1] concerning sums of the form $\Sigma f(t2^k)$ is also investigated. In proofs, limit theorems for differently distributed independent summands are used instead of the characteristic function method.
