Skip to main content
SpringerLink
Log in

An alternative representation of noncentral beta and F distributions

  • Notes
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

In this paper the doubly noncentral beta and F distributions are represented alternatively by using the results on the product of two hypergeometric functions. Their moments and the cumulative distribution functions are also given in terms of hypergeometric functions, which can be easily calculated by the Mathematica package.

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

References

  1. Chaundy TW(1943): An extension of hypergeometric functions. Quarter J. Math., Oxford ser. 14, 55–78.

    MATH  MathSciNet  Google Scholar 

  2. Erdéyi A, Magnu W, Oberhettinger F and Tricomi GO(1953): Higher Transcendental functions. Vol. I, McGraw Hill, New York.

    Google Scholar 

  3. Fisher RA(1928): The general sampling distribution of the multiple correlation coefficient. Proc. Roy. Soc. 121 A, 654–673.

    Google Scholar 

  4. Ghosh MN and Sharma D(1963): Power of Tukey's test for nonadditivity. J. Roy. Statist. Soc. 25 B, 213–219.

    MathSciNet  Google Scholar 

  5. Johnson NL, Kotz S and Balakrishnan N(1995): Continuous univariate distributions 2. John Wiley and Sons, New York.

    Google Scholar 

  6. Muirhead RJ(1982): Aspects of multivariate statistical theory. John Wiley and Sons, New York.

    MATH  Google Scholar 

  7. Rainville ED(1960): Special functions. Chelsea publishing Co., New York.

    MATH  Google Scholar 

  8. Scheffé H(1959): The Analysis of variance. John Wiley and Sons, New York.

    Google Scholar 

  9. Tang PC(1938): The power functions of the analysis of variance tests with tables and illustrations of their use. Statist. Res. Mem. 2, 126–157.

    MATH  Google Scholar 

  10. Pe T(1975): Analysis of functional relationships: Old and new models. Ph. D. Thesis, University of Melbourne, Australia.

    Google Scholar 

  11. Pe T(1982): Exact non-null distribution of a test of correlation in the context of functional relationship models. Preprint no. 2/82 Mathematical publications, University of Kassel, Germany.

    Google Scholar 

  12. Weibull M(1953): The distributions of t and F-statistics and the correlation and regression coefficients in stratified samples from normal populations with different means. Skand. Aktuar. 36, 9–106.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Quantitative Methods and Mathematical Sciences, University of Western Sydney, Locked Bag 1797, 1797, Penrith South, DC, Australia

    Than Pe

  2. Universität Kassel, Fachbereich 17 Mathematik/Informatik, 34109, Kassel, Germany

    Hilmar Drygas

Authors
  1. Than Pe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hilmar Drygas
    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

Pe, T., Drygas, H. An alternative representation of noncentral beta and F distributions. Statistical Papers 47, 311–318 (2006). https://doi.org/10.1007/s00362-005-0290-7

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-005-0290-7

Keywords and phrases

Search

Navigation