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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 1983, Number 3, Pages 11–20
(Mi vmumm3486)
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Mathematics
The property of extendability of limit distributions for the maximum term of a sequence
B. V. Gnedenko, L. Senusi-Bereksi
Abstract:
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.
Received: 09.11.1982
Citation:
B. V. Gnedenko, L. Senusi-Bereksi, “The property of extendability of limit distributions for the maximum term of a sequence”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1983, no. 3, 11–20
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https://www.mathnet.ru/eng/vmumm3486 https://www.mathnet.ru/eng/vmumm/y1983/i3/p11
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