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Teoriya Veroyatnostei i ee Primeneniya, 1956, Volume 1, Issue 4, Pages 437–465 (Mi tvp5012)  

This article is cited in 8 scientific papers (total in 8 papers)

Sequential Bayes Solutions and Optimal Methods of Statistical Acceptance Control

V. S. Mikhalevič

Kiev
Abstract: This paper gives a description of classes of sequential Bares solutions for the binomial family of distributions and for the Poisson process, if the weight function is monotonic and some of its zeros are points of increase for the a priori probability distribution. The corresponding Bares solutions are truncated with respect to $n$ (or $t$). These solutions are determined by the process of trial and error between two bounds. A risk function for a Poisson process is proved to satisfy certain differential equations. It is possible to determine the bounds of Bares solutions with the help of these equations.
The limiting theorem on the convergence of the boundaries of Bares solutions and the risk functions, when the corresponding binomial processes converge to a Poisson process, is proved. The results obtained are used in describing the class of optimum methods of statistical acceptance control.
Received: 06.11.1956
English version:
Theory of Probability and its Applications, 1956, Volume 1, Issue 4, Pages 395–421
DOI: https://doi.org/10.1137/1101031
Document Type: Article
Language: Russian
Citation: V. S. Mikhalevič, “Sequential Bayes Solutions and Optimal Methods of Statistical Acceptance Control”, Teor. Veroyatnost. i Primenen., 1:4 (1956), 437–465; Theory Probab. Appl., 1:4 (1956), 395–421
Citation in format AMSBIB
\Bibitem{Mik56}
\by V.~S.~Mikhalevi{\v{c}}
\paper Sequential Bayes Solutions and Optimal Methods of Statistical Acceptance Control
\jour Teor. Veroyatnost. i Primenen.
\yr 1956
\vol 1
\issue 4
\pages 437--465
\mathnet{http://mi.mathnet.ru/tvp5012}
\transl
\jour Theory Probab. Appl.
\yr 1956
\vol 1
\issue 4
\pages 395--421
\crossref{https://doi.org/10.1137/1101031}
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  • https://www.mathnet.ru/eng/tvp/v1/i4/p437
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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