An Asymptotically Distribution-Free Goodness-of-Fit Test for Families of Statistical Distributions Depending on Two Parameters

  • Fortunato Pesarin
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)


This paper concerns a general goodness-of-fit test for families of statistical distributions depending on two nuisance parameters and satisfying some general conditions. The null distribution of the test statistic does not depend on the nuisance parameters and is asymptotically distribution-free. The paper gives a short table of its critical values and a table of its power against some alternatives.

Key Words

Asymptotically distribution-free test goodness-of- fit test nuisance parameters families of statistical distributions weighted Cramér-von Mises test 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Csörgö, S., Stacho, L. (1980). A step toward an asymptotic expansion for the Cramér-von Mises statistic. In Colloquia Mathematica Societatis Janos Bolyai, Analytic Function Methods in Probability Theory, B. Gyres, ed. North- Holland Publishing Company, Amsterdam, Pages 53–65.Google Scholar
  2. Durbin, J. (1973). Distribution Theory for Tests Based on the Sample Distribution Function. SIAM, Philadelphia.Google Scholar
  3. Pesarin, F., Azzalini, A. (1976). Verifica di ipotesi funzionale non parametrica. In L’Elaborazione Automatica, 2, 53–77.Google Scholar
  4. Pesarin, F. (1977). A goodness-of-fit test for families of random variables depending on two parameters with censored data. Recent Developments in Statistics, I. R. Barra et al., ed. North Holland. Pages 567–570.Google Scholar
  5. Pesarin, F. (1978). Controllo statistico di curve di affidabalità dipendenti da due parametri. In Atti del Decimo Convegno Nazionale della Associazione Italiana per il Controllo della Qualità, 77–83. Google Scholar
  6. Pettitt, A.N. (1978). Generalized Cramer-von Mises statistics for the gamma distribution. Biometrika, 65, 232–235.MathSciNetzbMATHGoogle Scholar
  7. Sarkadi, K. (1975). The consistency of the Shapiro-Francia test. Biometrika, 62, 445–450.MathSciNetzbMATHGoogle Scholar
  8. Shapiro, S.S., Francia, R.S. (1972). Approximate analysis of variance test for normality. Journal of the American Statistical Association, 67, 215–225.CrossRefGoogle Scholar
  9. Stephens, M.A. (1974). EDF Statistic for goodness-of-fit and some comparisons. Journal of the American Statistical Association, 69, 730–737.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Fortunato Pesarin
    • 1
  1. 1.Institute of StatisticsUniversity of PadovaPadovaItaly

Personalised recommendations