Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 11-20
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B. V. Gnedenko; L. Senusi-Bereksi. The property of extendability of limit distributions for the maximum term of a sequence. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 11-20. http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a2/
@article{VMUMM_1983_3_a2,
author = {B. V. Gnedenko and L. Senusi-Bereksi},
title = {The property of extendability of limit distributions for the maximum term of a sequence},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {11--20},
year = {1983},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a2/}
}
TY - JOUR
AU - B. V. Gnedenko
AU - L. Senusi-Bereksi
TI - The property of extendability of limit distributions for the maximum term of a sequence
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 1983
SP - 11
EP - 20
IS - 3
UR - http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a2/
LA - ru
ID - VMUMM_1983_3_a2
ER -
%0 Journal Article
%A B. V. Gnedenko
%A L. Senusi-Bereksi
%T The property of extendability of limit distributions for the maximum term of a sequence
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 1983
%P 11-20
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a2/
%G ru
%F VMUMM_1983_3_a2
Let $\xi_1,\xi_2,\dots$ be a sequence of identically distributed independent random variables, and let $$ \eta_n=\max(\xi,\xi_2,\dots,\xi_n). $$ The following theorem is proved: If for a certain choice of constants $b_n>0$ and $a_n$$$ P\biggl\{\frac1{b_n}(\eta_n-a_n)<x\biggr\}\to\Phi(x),\quad n\to\infty, $$ where $\Phi(x)$ is one of the three possible limiting distributions, and if the convergence is fulfilled in an interval $(c,d)$ for which $\Phi(d)-\Phi(c)>0$, then the convergence holds for all values of $x$. Библиогр. 5.
