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Teor. Veroyatnost. i Primenen., 1965, Volume 10, Issue 4, Pages 672–692 (Mi tvp580)  

This article is cited in 1 scientific paper (total in 1 paper)

On a class of limit distributions for normed sums of independent random variables

A. A. Zinger

Leningrad

Abstract: Let $\zeta_n=\frac{\xi_1+\xi_2+…+\xi_n}{B_n}-A_n$ ($n=1,2,…$) be a sequence of normed sums $n$ of independent random variables which has a nondegenerate limit distribution $G(x)$ for appropriately selected constants $A_n$, $B_n$.
This paper is devoted to the characterization of the class $\{G(x)\}$ named here $\mathscr P_r$ arizing when among the distributions of the random variables $\xi^i$ there are only $r$ different ones. Three theorems describing the class $\mathscr P_r$ are proved

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English version:
Theory of Probability and its Applications, 1965, 10:4, 607–626

Bibliographic databases:

Received: 18.05.1965

Citation: A. A. Zinger, “On a class of limit distributions for normed sums of independent random variables”, Teor. Veroyatnost. i Primenen., 10:4 (1965), 672–692; Theory Probab. Appl., 10:4 (1965), 607–626

Citation in format AMSBIB
\Bibitem{Zin65}
\by A.~A.~Zinger
\paper On a~class of limit distributions for normed sums of independent random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 4
\pages 672--692
\mathnet{http://mi.mathnet.ru/tvp580}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=195137}
\zmath{https://zbmath.org/?q=an:0235.60021}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 4
\pages 607--626
\crossref{https://doi.org/10.1137/1110076}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. A. Lifshits, Ya. Yu. Nikitin, V. V. Petrov, A. Yu. Zaitsev, A. A. Zinger, “Toward the history of the Saint Petersburg school of probability and statistics. I. Limit theorems for sums of independent random variables”, Vestn. St Petersb. Univ. Math., 51:2 (2018), 144–163  crossref  crossref  mathscinet  zmath  isi  elib  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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