Skip to main content

Part of the book series: Lecture Notes in Statistics ((LNS,volume 114))

  • 459 Accesses

Summary

In 1958 H.T. David defined a statistic for testing the hypothesis that three samples of equal size n are drawn from the same continuous distribution. In this paper explicit formulas are given for the distribution and the asymptotic distribution of this statistic.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L.C. Chang and M. Fisz: Asymptotically independent linear functions of empirical distribution functions. Science Record 1 (1957) 335–340.

    MathSciNet  MATH  Google Scholar 

  2. L.C. Chang and M. Fisz: Exact distributions of the maximal values of some functions of empirical distribution functions. Science Record 1 (1957) 341–346.

    MathSciNet  MATH  Google Scholar 

  3. H.T. David: A three-sample Kolmogorov-Smirnov test. The Annals of Mathematical Statistics 29 (1958) 842–851.

    Article  MATH  Google Scholar 

  4. L.E. Dickson: Introduction to the Theory of Numbers. University of Chicago Press, 1929. [Reprinted by Dover, New York, 1957.]

    MATH  Google Scholar 

  5. P.G. Lejeune Dirichlet: Vorlesungen über Zahlentheorie. Fourth edition. Braunschweig, 1893. [Reprinted by Chelsea, New York, 1968.]

    Google Scholar 

  6. M. Fisz: A limit theorem for empirical distribution functions. Bulletin de l’Académie Polonaise des Sciences Cl. III. 5 (1957) 695–698.

    MathSciNet  MATH  Google Scholar 

  7. M. Fisz: A limit theorem for empirical distribution functions. Studia Mathematica 17 (1958) 71–77.

    MathSciNet  MATH  Google Scholar 

  8. M. Fisz: Some non-parametric tests for the k- sample problem. Colloquium Mathematicum 7 (1960) 289–296.

    MathSciNet  MATH  Google Scholar 

  9. I.I. Gikhman: On a nonparametric homogeneity criterion forksamples. Theory of Probability and its Applications 2 (1957) 369–373.

    Article  Google Scholar 

  10. B.V. Gnedenko and V.S. Korolyuk: On the maximum discrepancy between two empirical distributions. (Russian) Doklady Akademii Nauk SSSR 80 (1951) 525–528. [English translation: Selected Translations in Mathematical Statistics and Probability. Vol. 1. American Mathematical Society, Providence, RI, 1961, pp. 13–16.]

    MathSciNet  MATH  Google Scholar 

  11. S. Karlin and J. McGregor: Coincidence probabilities. Pacific Journal of Mathematics 9 (1959) 1141–1164.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Kiefer: K-sample analogues of the Kolmogorov-Smirnov and Cramér-v. Mises tests. The Annals of Mathematical Statistics 30 (1959) 420–447.

    Article  MathSciNet  MATH  Google Scholar 

  13. A. Kolmogoroff: Sulla determinazione empirica di una legge di distribuzione. Giornale dell’ Istituto Italiano degli Attuari 4 (1933) 83–91.

    Google Scholar 

  14. E. Landau: Elementary Number Theory. Chelsea, New York, 1958.

    Google Scholar 

  15. V. Ozols: Generalization of the theorem of Gnedenko-Korolyuk to three samples in the case of two one-sided boundaries. (Latvian. Russian summary) Latvijas PSR Zinátgu Akadémijas Véstis. No. 10 (111) (1956) 141–152.

    Google Scholar 

  16. N.V. Smirnov: On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bulletin Mathématique de l’Universté de Moscou. Série Internationale. 2 No. 2 (1939) 3–16.

    Google Scholar 

  17. S. Wolfram: Mathematica. A System for Doing Mathematics by Computer. Second edition. Addison-Wesley, Redwood City, California, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer Science+Business Media New York

About this paper

Cite this paper

Takács, L. (1996). On a Three-Sample Test. In: Heyde, C.C., Prohorov, Y.V., Pyke, R., Rachev, S.T. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0749-8_31

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0749-8_31

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94788-4

  • Online ISBN: 978-1-4612-0749-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics