Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 557-570
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G. I. Ivchenko. Variational series for the scheme of summing independent variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 557-570. http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a10/
@article{TVP_1973_18_3_a10,
author = {G. I. Ivchenko},
title = {Variational series for the scheme of summing independent variables},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {557--570},
year = {1973},
volume = {18},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a10/}
}
TY - JOUR
AU - G. I. Ivchenko
TI - Variational series for the scheme of summing independent variables
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1973
SP - 557
EP - 570
VL - 18
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a10/
LA - ru
ID - TVP_1973_18_3_a10
ER -
%0 Journal Article
%A G. I. Ivchenko
%T Variational series for the scheme of summing independent variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1973
%P 557-570
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a10/
%G ru
%F TVP_1973_18_3_a10
Let $\xi_1,\dots,\xi_N$ be $N$ independent observations of a random variable $\xi$ and $\xi_{(m)}$ be the $m$th order statistic of this sample. We study the asymptotic behaviour of $\xi_{(m)}$ and $\xi_{(N-m+1)}$ when the distribution of $\xi$ is a convolution of $n$ identical distributions and $n,N\to\infty$.
