Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 1983, Number 3, Pages 11–20 (Mi vmumm3486)  

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
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
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
Citation in format AMSBIB
\Bibitem{GneSen83}
\by B.~V.~Gnedenko, L.~Senusi-Bereksi
\paper The property of extendability of limit distributions for the maximum term of a sequence
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 1983
\issue 3
\pages 11--20
\mathnet{http://mi.mathnet.ru/vmumm3486}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=0705594}
\zmath{https://zbmath.org/?q=an:0518.60028}
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