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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 575–582 (Mi tvp743)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

On the number of observations necessary for the distinction between two proximate hypotheses

I. N. Volodin

Kazan

Abstract: The problem of distinction between the following two proximate hypotheses $\mathbf H_0$: the population density is equal to $p_0(x)$ and $\mathbf H_\alpha$: the population density is equal to $p_\alpha(x)$, where $p_\alpha(x)\to p_0(x)$ as $\alpha\to0$, using the results of independent observations is considered.
In the case when $\alpha$ is a one dimensional parameter the Petrov–Aivazyan formula [1] for the number of observations nesessary for the distinction between hypotheses $\mathbf H_0$ and $\mathbf H_\alpha$ according to the Neumann–Pearson criterion with given probabilities of errors of the first $(\varepsilon)$ and second $(\omega)$ type is improved up to the members of order $O(1)$. A possibility of application of the results of this article to the problem of testing the hypotheses on the types of distributions given a large number of small simples is demonstrated by the example of the distinction between two gamma-types.

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English version:
Theory of Probability and its Applications, 1967, 12:3, 519–525

Bibliographic databases:

Received: 17.02.1966

Citation: I. N. Volodin, “On the number of observations necessary for the distinction between two proximate hypotheses”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 575–582; Theory Probab. Appl., 12:3 (1967), 519–525

Citation in format AMSBIB
\Bibitem{Vol67}
\by I.~N.~Volodin
\paper On the number of observations necessary for the distinction between two proximate hypotheses
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 3
\pages 575--582
\mathnet{http://mi.mathnet.ru/tvp743}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=219174}
\zmath{https://zbmath.org/?q=an:0168.39802}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 3
\pages 519--525
\crossref{https://doi.org/10.1137/1112066}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. A. Dzhungurova, I. N. Volodin, “The asymptotic of the necessary sample size in testing the hypotheses on the shape parameter of a distribution close to the normal one”, Russian Math. (Iz. VUZ), 51:5 (2007), 44–50  mathnet  crossref  mathscinet  zmath
    2. A. A. Zaikin, “Defect of the size of nonrandomized test and randomization effect on the necessary sample size in testing the Bernoulli success probability”, Theory Probab. Appl., 59:3 (2015), 466–480  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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