Geodesic
On Uniform Approximation of the Binomial Distribution by Infinitely Divisible Laws
Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 470-474

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@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},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1958},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a9/
%G ru
%F TVP_1958_3_4_a9
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/