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On a test for goodness-of-fit based on the empirical probability measure of Foutz and testing for exponentiality

  • Miklós Csörgő
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)

Abstract

Foutz (1979) proposed a goodness-of-fit test for the simple hypothesis specifying a continuous p-variate distribution Open image in new window . For a suitably defined empirical probability measure, Open image in new window , the proposed test is based on the supremum of the absolute differences between hypothesized and empirical probabilities, the supremum being taken over all possible events. He showed that his test statistic was distribution free in the general p-variate case and derived its asymptotic null distribution. Here an alternate quick way of deriving the latter is proposed and connections are made to testing for exponentiality.

Keywords

Brownian Bridge Quantile Process Equivalent Block Mise Type Borel Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Anderson, T.W. (1966). Some nonparametric procedures based on statistically equivalent blocks. Proc. Internat. Symp. Multivariate Anal. (P.R. Krishnaiah, ed.). 5–27, Academic Press, New York.Google Scholar
  2. [2]
    Csörgő, M.-Révész, P. (1978). Strong approximations of the quantile process. Ann. Statist. 6, 882–894.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Csörgő, M.-Révész, P. (1979). Quadratic...ity tests. Carleton Mathematical Series No. 162. A revised version is to appear.Google Scholar
  4. [4]
    Csörgő, M., Seshadri, V. and Yalovsky, M. (1975). Applications of characterizations in the area of goodness-of-fit. In Statistical Distributions in Scientific Work, Vol. 2, 79–90, eds. G.P. Patil et al. D. Reidel Publishing Co., Dordrecht-Holland.CrossRefGoogle Scholar
  5. [5]
    Foutz, Robert V. (1979). A test for goodness-of-fit based on an empirical probability measure. To appear.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Miklós Csörgő
    • 1
  1. 1.Department of Mathematics and StatisticsCarleton UniversityOttawa

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