Skip to main content
SpringerLink
Log in

Scharfe untere und obere Schranken für die Wahrscheinlichkeit der Realisation vonk untern Ereignissen

  • Published:
Metrika Aims and scope Submit manuscript

Summary

LetA 1,...,A n be events in a probability space (Ω,A,W). We denote byL k the event, that at leastk events among then eventsA 1,...A n occur, and byK k the event, that exactlyk events occur. If only the inequalities α i ⩽W(A i )⩽β i ,i=1,...,n, are known, we calculate sharp lower and upper bounds forW(L k ) andW(K k ). These bounds only depend onn, k and α i ,β i ,i=1,...,n. They are relevant, when treating combined tests or confidence procedures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literaturverzeichnis

  • Boole, G.: Laws of Thought. Amer. reprint of 1854. New York

  • Feller, W.: An Introduction to probability Theory and its Applications, Band 1, 3. Auflage. New York-London-Sydney 1968.

  • Galambos, J.: Bonferroni Inequalities. Annals of Probability5, 1977, 577–581.

    Article  MathSciNet  MATH  Google Scholar 

  • Hailperin, T.: Best Possible Inequalities for the Probability of a Logical Function of Events. Am. Math. Monthly72, 1965, 343–359.

    Article  MathSciNet  MATH  Google Scholar 

  • Hommel, G.: Entwicklung einer statistischen Teststrategie für komplexe medizinische Fragestellungen. Habilitationsschrift. Erlangen 1979.

  • Koziol, J.A. undM.D. Perlman: Combining Independent Chi-Squared Tests. J. Amer. Statist. Assoc.73, 1978, 753–763.

    Article  MATH  Google Scholar 

  • Kwerel, S.M.: Most stringent bounds on aggregated probabilities of partially specified dependent probability systems. J. Amer. Statist. Assoc.70, 1975, 472–479.

    Article  MathSciNet  MATH  Google Scholar 

  • Miller, R.G., Jr.: Developments in Multiple Comparisons 1966–1976. J. Amer. Statist. Assoc.72, 1977, 779–788.

    MathSciNet  MATH  Google Scholar 

  • Morgenstern, D.: Berechnung des maximalen Signifikanzniveaus des Testes “LehneH 0 ab, wennk untern gegebenen Tests zur Ablehnung führen”. Metrika27, 1980, 285–286.

    Article  MathSciNet  MATH  Google Scholar 

  • Rényi, A.: Foundations of Probability. San Francisco 1970.

  • Rüger, B.: Das maximale Signifikanzniveau des Tests: “LehneH 0 ab, wennk untern gegebenen Tests zur Ablehnung führen”. Metrika25, 1978, 171–178.

    Article  MathSciNet  MATH  Google Scholar 

  • Skrøppa, T.: Some Monte Carlo results concerning the probability of false rejections for a multiple hypotheses testing problem. Stat. Res. Report, No. 2, Dep. of Mathematics, Univ. of Oslo, 1974.

  • Spjøtvoll, E.: Multiple Testing in the Analysis of Variance. Scand. J. Statist.1, 1974, 97–114.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Statistik und Wissenschaftstheorie der Universität München, Ludwigstraße 33/I, D-8000, München 22

    B. Von Rüger (Priv.-Doz.)

Authors
  1. B. Von Rüger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Von Rüger, B. Scharfe untere und obere Schranken für die Wahrscheinlichkeit der Realisation vonk untern Ereignissen. Metrika 28, 71–77 (1981). https://doi.org/10.1007/BF01902879

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01902879

Search

Navigation