Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 218-228
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J. J. Mačys. Estimations in the theorem of the stability of Poisson distribution decompositions. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 218-228. http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a1/
@article{TVP_1971_16_2_a1,
author = {J. J. Ma\v{c}ys},
title = {Estimations in the theorem of the stability of {Poisson} distribution decompositions},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {218--228},
year = {1971},
volume = {16},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a1/}
}
TY - JOUR
AU - J. J. Mačys
TI - Estimations in the theorem of the stability of Poisson distribution decompositions
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1971
SP - 218
EP - 228
VL - 16
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a1/
LA - ru
ID - TVP_1971_16_2_a1
ER -
%0 Journal Article
%A J. J. Mačys
%T Estimations in the theorem of the stability of Poisson distribution decompositions
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
%P 218-228
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a1/
%G ru
%F TVP_1971_16_2_a1
Let $\Pi_\lambda$ be a Poisson distribution function and $F=F_1*F_2$ a distribution function such that either in the Lévy metric or in the uniform metric $\rho(F,\Pi_\lambda)\le\varepsilon$. We show that, there exists a Poisson distribution function $\Pi_{\lambda_1}$ such that $$ \rho(F_1,\Pi_{\lambda_1})<C(\lambda)\sqrt{\frac{\ln(-\ln\varepsilon)}{(-\ln\varepsilon)}}. $$
