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

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

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:

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
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
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