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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 4, Pages 741–746 (Mi tvp763)

Short Communications

On the distribution of the statistic of the most powerful test in compound Markov chains

P. F. Belyaev

Moscow

Abstract: The paper deals with a sequence of outcomes realized after $n$ tests, connected into a compound Markov chain of order $s-1$ with $k$ states and with the transition probabilities of the form $1/k+\alpha/k\varphi(k)$ where $\varphi(k)$ as $k\to\infty$ and $|\alpha|<C$.
The statistic of the most powerful test for two simple hypotheses concerning the values of $\alpha$ is considered and some asymptotic properties of this statistic are studied as $n$, $k\to\infty$.

Full text: PDF file (379 kB)

English version:
Theory of Probability and its Applications, 1967, 12:4, 678–682

Bibliographic databases:

Citation: P. F. Belyaev, “On the distribution of the statistic of the most powerful test in compound Markov chains”, Teor. Veroyatnost. i Primenen., 12:4 (1967), 741–746; Theory Probab. Appl., 12:4 (1967), 678–682

Citation in format AMSBIB
\Bibitem{Bel67} \by P.~F.~Belyaev \paper On the distribution of the statistic of the most powerful test in compound Markov chains \jour Teor. Veroyatnost. i Primenen. \yr 1967 \vol 12 \issue 4 \pages 741--746 \mathnet{http://mi.mathnet.ru/tvp763} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=225419} \zmath{https://zbmath.org/?q=an:0178.21701} \transl \jour Theory Probab. Appl. \yr 1967 \vol 12 \issue 4 \pages 678--682 \crossref{https://doi.org/10.1137/1112084}