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Teor. Veroyatnost. i Primenen., 1971, Volume 16, Issue 1, Pages 118–131 (Mi tvp1973)  

The limit distribution of the extreme terms of the variational series under the large deviation type conditions for the sample mean .

A. V. Nagaev

Tashkent

Abstract: Let $x_1,…x_n$ 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 $x_1+…+x_n$ is large.

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English version:
Theory of Probability and its Applications, 1971, 16:1, 126–140

Bibliographic databases:

Received: 16.06.1969

Citation: A. V. Nagaev, “The limit distribution of the extreme terms of the variational series under the large deviation type conditions for the sample mean .”, Teor. Veroyatnost. i Primenen., 16:1 (1971), 118–131; Theory Probab. Appl., 16:1 (1971), 126–140

Citation in format AMSBIB
\Bibitem{Nag71}
\by A.~V.~Nagaev
\paper The limit distribution of the extreme terms of the variational series under the large deviation type conditions for the sample mean .
\jour Teor. Veroyatnost. i Primenen.
\yr 1971
\vol 16
\issue 1
\pages 118--131
\mathnet{http://mi.mathnet.ru/tvp1973}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=285041}
\zmath{https://zbmath.org/?q=an:0244.60018}
\transl
\jour Theory Probab. Appl.
\yr 1971
\vol 16
\issue 1
\pages 126--140
\crossref{https://doi.org/10.1137/1116009}


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