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Some New Goodness‐Of‐Fit Tests Using Order Statistics

Author

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  • Y. A. S. Hegazy
  • J. R. Green

Abstract

Some new tests of the goodness of fit of the uniform and of the normal distribution (both with unknown parameters) to given data are presented and the distributions of some of them are obtained approximately; also critical values are obtained by simulation. Approximate relationships for the dependence of the critical values of the test criterion upon n, the sample size, are derived, so that n need not be involved in the tabulation. The powers of the tests under certain alternatives are examined. They are found to be among the most powerful tests available for the hypotheses concerned.

Suggested Citation

  • Y. A. S. Hegazy & J. R. Green, 1975. "Some New Goodness‐Of‐Fit Tests Using Order Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(3), pages 299-308, November.
    • Handle: RePEc:bla:jorssc:v:24:y:1975:i:3:p:299-308
    DOI: 10.2307/2347090
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    Cited by:

    1. Anthony Medford & James W. Vaupel, 2020. "Extremes are not normal: a reminder to demographers," Journal of Population Research, Springer, vol. 37(1), pages 91-106, March.
    2. Fernández-de-Marcos, Alberto & García-Portugués, Eduardo, 2023. "Data-driven stabilizations of goodness-of-fit tests," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    3. Mengta Yang & Reza Modarres, 2017. "Multivariate tests of uniformity," Statistical Papers, Springer, vol. 58(3), pages 627-639, September.
    4. H. J. Khamis, 2000. "The two-stage i -corrected Kolmogorov-Smirnov test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(4), pages 439-450.
    5. J. S. Allison & L. Santana & N. Smit & I. J. H. Visagie, 2017. "An ‘apples to apples’ comparison of various tests for exponentiality," Computational Statistics, Springer, vol. 32(4), pages 1241-1283, December.
    6. Fernández de Marcos Giménez de los Galanes, Alberto, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.

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