Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 3, pp. 522-525
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S. G. Maloshevskii. Unimprovability of the result due to N. A. Sapogov in the stability problem of Cramér's theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 3, pp. 522-525. http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a14/
@article{TVP_1968_13_3_a14,
author = {S. G. Maloshevskii},
title = {Unimprovability of the result due to {N.} {A.~Sapogov} in the stability problem of {Cram\'er's} theorem},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {522--525},
year = {1968},
volume = {13},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a14/}
}
TY - JOUR
AU - S. G. Maloshevskii
TI - Unimprovability of the result due to N. A. Sapogov in the stability problem of Cramér's theorem
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1968
SP - 522
EP - 525
VL - 13
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a14/
LA - ru
ID - TVP_1968_13_3_a14
ER -
%0 Journal Article
%A S. G. Maloshevskii
%T Unimprovability of the result due to N. A. Sapogov in the stability problem of Cramér's theorem
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1968
%P 522-525
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a14/
%G ru
%F TVP_1968_13_3_a14
We consider the sequence (1) of compositions of distribution functions satisfying the condition (2). Let truncated variances of components be bounded from below by a positive constant. It is proved that the well-known estimate $$ \max_{i=1,2}\inf_{G\in N}\sup_x|F_n^{(i)}(x)-G(x)|=O\biggl(\frac1{\sqrt{-\ln\varepsilon_n}}\biggr) $$ (where $N$ is the set of all normal distribution functions) is unimprovable.
