RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 206–210 (Mi tvp2705)  

Short Communications

Experiment design for comparison of two normal population parameters

I. N. Volodin

Кazan

Abstract: Two normal population with parameters ($m_1$, $\sigma_1$) and ($m_2$, $\sigma_2$) are given, three pairs of alternative hypotheses being considered:
1) $H_0\colon m_1-m_2=0$, $H_1\colon m_1-m_2\ge\Delta$;
2) $H_0\colon m_1-m_2=0$, $H_1\colon|m_1-m_2|\ge\Delta$;
3) $H_0\colon\sigma_1^2/\sigma_2^2\le k$, $H_1\colon\sigma_1^2/\sigma_2^2\ge k(1+\Delta)$.
Given error probabilities of the first ($\alpha$) and the second kind ($\beta$), two-step procedures are constructed for the first two pairs of hypotheses which enable to determine how many extra observations are needed for the given procedures to have the strength ($\alpha$, $\beta$), the initial ($n_0$, $N_0$) observations being available. These tests have been obtained as a result of applying Stein's procedure to the Bartlette-Scheffe and Student's test.
For the third pair of hypotheses, an asymptotic formula is proposed for the number of observations necessary for Fisher's test to have a given strength ($\alpha$, $\beta$).

Full text: PDF file (434 kB)

English version:
Theory of Probability and its Applications, 1973, 18:1, 198–202

Bibliographic databases:

Received: 20.01.1971

Citation: I. N. Volodin, “Experiment design for comparison of two normal population parameters”, Teor. Veroyatnost. i Primenen., 18:1 (1973), 206–210; Theory Probab. Appl., 18:1 (1973), 198–202

Citation in format AMSBIB
\Bibitem{Vol73}
\by I.~N.~Volodin
\paper Experiment design for comparison of two normal population parameters
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 1
\pages 206--210
\mathnet{http://mi.mathnet.ru/tvp2705}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=317466}
\zmath{https://zbmath.org/?q=an:0277.62017}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 18
\issue 1
\pages 198--202
\crossref{https://doi.org/10.1137/1118022}


Linking options:
  • http://mi.mathnet.ru/eng/tvp2705
  • http://mi.mathnet.ru/eng/tvp/v18/i1/p206

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:73
    Full text:47

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020