Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 1, pp. 118-131
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A. V. Nagaev. The limit distribution of the extreme terms of the variational series under the large deviation type conditions for the sample mean .. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 1, pp. 118-131. http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a8/
@article{TVP_1971_16_1_a8,
author = {A. V. Nagaev},
title = {The limit distribution of the extreme terms of the variational series under the large deviation type conditions for the sample mean .},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {118--131},
year = {1971},
volume = {16},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a8/}
}
TY - JOUR
AU - A. V. Nagaev
TI - The limit distribution of the extreme terms of the variational series under the large deviation type conditions for the sample mean .
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1971
SP - 118
EP - 131
VL - 16
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a8/
LA - ru
ID - TVP_1971_16_1_a8
ER -
%0 Journal Article
%A A. V. Nagaev
%T The limit distribution of the extreme terms of the variational series under the large deviation type conditions for the sample mean .
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
%P 118-131
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a8/
%G ru
%F TVP_1971_16_1_a8
Let $x_1,\dots x_n$ be independent observations of a random variable $\xi$, $\underline x=\min\limits_{1\le i\le n}x_i$, $\overline x=\max\limits_ {1\le i\le n}x_i$. Some theorems are proved concerning the distribution of $\underline x$ and $\overline x$ under the condition that the sum $x_1+\dots+x_n$ is large.
