Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 470-474
Citer cet article
I. P. Tsaregradskii. On Uniform Approximation of the Binomial Distribution by Infinitely Divisible Laws. Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 470-474. http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a9/
@article{TVP_1958_3_4_a9,
author = {I. P. Tsaregradskii},
title = {On {Uniform} {Approximation} of the {Binomial} {Distribution} by {Infinitely} {Divisible} {Laws}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {470--474},
year = {1958},
volume = {3},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a9/}
}
TY - JOUR
AU - I. P. Tsaregradskii
TI - On Uniform Approximation of the Binomial Distribution by Infinitely Divisible Laws
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1958
SP - 470
EP - 474
VL - 3
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a9/
LA - ru
ID - TVP_1958_3_4_a9
ER -
%0 Journal Article
%A I. P. Tsaregradskii
%T On Uniform Approximation of the Binomial Distribution by Infinitely Divisible Laws
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1958
%P 470-474
%V 3
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a9/
%G ru
%F TVP_1958_3_4_a9
Let $F_p^n(x)$ be an $(n,p)$ –- binomial distribution function and be the set of all infinitely divisible laws. We define $$\rho\bigl(F_p^n,\mathfrak G\bigr)=\inf_{G\in\mathfrak G}\sup_x\left|F_p^n (x)-G(x)\right|.$$ Then, $$\sup_{0\leq p\leq1}\rho\left(F_p^n,\mathfrak G\right)<\frac{C_0}{\sqrt n},$$ where $C_0$ is an absolute constant.
