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Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 3, Pages 534–537 (Mi tvp652)  

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

Short Communications

The problem of choice and the optimal stopping rule for a sequence of random trials

S. M. Gusein-Zade

Moscow

Abstract: Suppose we have to choose an element from a finite set $A$ which consist of $n$ elements. Let $A$ be ordered by quality. We regard our choice as successful if the selected element is one of the best $r$ elements of $A$. Let us enumerate the elements of $A$ in such order as we learn them. After learning at we know the comparative qualities of $a_1,a_2,…,a_t$ but we know nothing about the quality of the remaining $n-t$ elements of $A$. While learning $a_t$ we can either accept it (then the choice is made) or reject it (then it will be impossible to return to it). We describe the optimal policy which secures the greatest probability of the successful choice and describe its asymptotical behaviour as $n\to\infty$.

Full text: PDF file (296 kB)

English version:
Theory of Probability and its Applications, 1966, 11:3, 472–476

Bibliographic databases:

Received: 13.12.1965

Citation: S. M. Gusein-Zade, “The problem of choice and the optimal stopping rule for a sequence of random trials”, Teor. Veroyatnost. i Primenen., 11:3 (1966), 534–537; Theory Probab. Appl., 11:3 (1966), 472–476

Citation in format AMSBIB
\Bibitem{Gus66}
\by S.~M.~Gusein-Zade
\paper The problem of choice and the optimal stopping rule for a~sequence of random trials
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 3
\pages 534--537
\mathnet{http://mi.mathnet.ru/tvp652}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=202256}
\zmath{https://zbmath.org/?q=an:0203.20405}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 3
\pages 472--476
\crossref{https://doi.org/10.1137/1111050}


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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. Sergei I. Dotsenko, Anna A. Ivashko, “O modelyakh nailuchshego dvustoronnego dvukhetapnogo vzaimnogo vybora”, MTIP, 9:1 (2017), 45–61  mathnet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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