Skip to main content
SpringerLink
Log in

A quick and easy approximation to the distribution of a sum of weighted chi-square variables

  • Algorithms
  • Published:
Statistische Hefte Aims and scope Submit manuscript

Abstract

Various statistical inferences related to chi-square tests lead to the problem of evaluating the probability of a weighted sum of chi-square variables.

Tables are available only for some special cases and the computation of the exact probabilities is very complicated due to the well-known problems of numerical integration. This paper presents the theoretical approach of an approximation and an easily implementable algorithm.

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

  • Callebaut, D.K. (1965). Generalizations of the Cauchy-Schwarz inequality. J. Math. Anal. Appl. 12, 491–494

    Article  MATH  MathSciNet  Google Scholar 

  • Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol II. John Wiley & Sons, New York

    MATH  Google Scholar 

  • Johnson N.L. and S. Kotz (1970). Continuous univariate distributions—2. Houghton Mifflin Company, Boston

    Google Scholar 

  • Lau, C.L. (1980). A Simple Series for the Incomplete Gamma Integral. Applied Statistics, 29, 113–114, Algorithm AS 147

    Article  MATH  Google Scholar 

  • Marshall, A.W. and J. Olkin (1979). Inequalities: Theory of Majorization and Its Applications. Academic Press, New York

    MATH  Google Scholar 

  • Mitrinović, D.S. (1970). Analytic Inequalities. Springer Verlag, Berlin

    Google Scholar 

  • Solomon H. and M.A. Stephens (1977). Distribution of a Sum of Weighted Chi-Square Variables. J. Americ. Statist. Assoc. 72, 881–885.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Seminar für Statistik, Universität Mannheim, A 5, 6800, Mannheim, West-Germany

    Siegfried Gabler & Christian Wolff

Authors
  1. Siegfried Gabler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Wolff
    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

Gabler, S., Wolff, C. A quick and easy approximation to the distribution of a sum of weighted chi-square variables. Statistische Hefte 28, 317–325 (1987). https://doi.org/10.1007/BF02932611

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02932611

Keywords

Search

Navigation