Skip to main content
SpringerLink
Log in

A non standard χ2-test of fit for testing uniformity with unknown limits

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

Abstract

A χ2-test of fit for testingH 0 “X∼U(a,b), a,b unknown” is suggested. It is nonstandard because the usual regularity assumptions are not satisfied. The asymptotic distribution of the test statistic underH 0 is derived. The error probabilities of the first kind are investigated by Monte Carlo simulation for samples of small and medium size.

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

  • Chernoff, H., Lehmann, E. L. (1954) The use of Maximum Likelihood Estimates in χ2-tests for goodness of fit, Ann. Math. Stat. 25, 579–586

    Article  MathSciNet  Google Scholar 

  • Cramer, H. (1946) Mathematical Methods of Statistics, Princeton, Princeton University Press

    MATH  Google Scholar 

  • D’Agostino, R. B., Stephens, M. A. (1986) Goodness-of-Fit Techniques, New York, Marcel Dekker Inc.

    MATH  Google Scholar 

  • David, H. A. (1970) Order Statistics, New York, John Wiley & Sons Inc.

    MATH  Google Scholar 

  • Kotz, S., Johnson, N. L. (1982) Encyclopedia of Statistical Sciences, New York, John Wiley & Sons

    MATH  Google Scholar 

  • Rao, C. R. (1973) Linear Statistical Inference and Its Applications (Second Edition), New York, John Wiley & Sons

    MATH  Google Scholar 

  • Watson, G. S. (1958) On chi-square goodness-of-fit tests for continuous distributions, J. R. Stat. Soc. Series B, 20, 44–61

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Statistik und Quantitative Ökonomik, Universität der Bundeswehr Hamburg, Holstenhofweg 85, D-22043, Hamburg, Deutschland

    Wolf Krumbholz

  2. Seminar für Wirtschafts- und Sozialstatistik, Universität zu Köln Albertus-Magnus-Platz, D-50923, Köln, Deutschland

    Friedrich Schmid

Authors
  1. Wolf Krumbholz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Friedrich Schmid
    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

Krumbholz, W., Schmid, F. A non standard χ2-test of fit for testing uniformity with unknown limits. Statistical Papers 37, 365–373 (1996). https://doi.org/10.1007/BF02926114

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02926114

Keywords

Search

Navigation