On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 625-636
Citer cet article
A. Yu. Zaitsev. On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 625-636. http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a0/
@article{TVP_1983_28_4_a0,
author = {A. Yu. Zaitsev},
title = {On the accuracy of approximation of distributions of sums of independent random variables~{\textendash} which are nonzero with a~small probability~{\textendash} by means of accompanying laws},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {625--636},
year = {1983},
volume = {28},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a0/}
}
TY - JOUR
AU - A. Yu. Zaitsev
TI - On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1983
SP - 625
EP - 636
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a0/
LA - ru
ID - TVP_1983_28_4_a0
ER -
%0 Journal Article
%A A. Yu. Zaitsev
%T On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1983
%P 625-636
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a0/
%G ru
%F TVP_1983_28_4_a0
Let $G_i=(1-p_i)E+p_iB_i$ where $0\le p_i\le 1$, $E$ is the distribution concentrated at zero, $B_i$ is an arbitrary one-dimensional distribution, $\displaystyle p=\max_{1\le i\le n}p_i$. Define $$ G=\prod_{i=1}^nG_i,\qquad D=\prod_{i=1}^n\exp(G_i-E). $$ Then $$ \sup_x|G\{(-\infty,x)\}-D\{(-\infty,x)\}|\le cp. $$
