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Comparison of Five Tests of Fit for the Extreme Value Distribution

  • D. J. Best
  • J. C. W. Rayner
  • O. Thas
Article

Abstract

Tests for the Extreme Value distribution based on the sample skewness and kurtosis coefficients are shown to be related to components of smooth tests of goodness of fit and are compared with tests due to Anderson-Darling, Shapiro-Brain and Liao-Shimokawa. Two examples are given.

AMS Subject Classification

62F03 and 62G32 

Keywords

Method of moments estimation Orthonormal functions Skewness and kurtosis coefficients Skewed distributions Weibull distribution 

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References

  1. Coles, S., 2004. An Introduction to Statistical Modelling of Extreme Values. Springer, New York.Google Scholar
  2. Gajek, L., 1986. On improving density estimates which are not bone fide functions. Ann. Statist. 14, 1612–1618.MathSciNetCrossRefGoogle Scholar
  3. Gürtler, N., Henze, N., 2000. Recent and classical goodness-of-fit tests for the Poisson distribution. Journal of Statistical Planning and Inference, 90, 207–225.MathSciNetCrossRefGoogle Scholar
  4. Henze, N., Klar, B., 1996. Properly rescaled components of smooth tests of fit are diagnostic. Austral. J. Statist. 38, 61–74.MathSciNetCrossRefGoogle Scholar
  5. IMSL, 1995. Fortran Numerical Libraries. Visual Numerics, Houston.Google Scholar
  6. Klar, B., 2000. Diagnostic smooth tests of fit. Metrika 52, 237–252.MathSciNetCrossRefGoogle Scholar
  7. Lancaster, H.O., 1969. The Chi-Squared Distribution. Wiley, New York.MATHGoogle Scholar
  8. Karlin, S., Altschul, S.F., 1990. Methods for assessing the statistical significance of molecular sequence features using general scoring schemes. Proc. Math. Acad. Sci. USA, 87, 2264–2268.CrossRefGoogle Scholar
  9. Liao, M., Shimokawa, T., 1999. A new goodness of fit test for Type-I Extreme-Value and Weibull distributions with estimated parameters. Journal of Statistical Computation and Simulation 64, 23–48.MathSciNetCrossRefGoogle Scholar
  10. Pal, N., Chun, J., Wooi, K.L., 2006. Handbook of Exponential and Related Distributions for Engineers and Scientists. Chapman and Hall/CRC, Boca Raton.MATHGoogle Scholar
  11. Rayner, J.C.W., Best, D.J., 1989. Smooth Tests of Goodness of Fit. Oxford University Press, New York.MATHGoogle Scholar
  12. Rayner, J.C.W., Best, D.J., Mathews, K.L., 1995. Interpreting the skewness coefficient. Commun. Statist.-Theor. Meth. 24(3), 593–600.CrossRefGoogle Scholar
  13. Shapiro, S.S., Brain, C.W., 1987. W-test for the Weibull distribution. Communications in Statistics — Simulation and Computation 16, 209–219.MathSciNetCrossRefGoogle Scholar
  14. Smith, R.L., Naylor, J.C., 1987. A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, 36 358–369.MathSciNetCrossRefGoogle Scholar
  15. Stephens, M.A., 1977. Goodness of fit for the extreme value distribution. Biometrika 64, 583–588.MathSciNetCrossRefGoogle Scholar
  16. Stuart, A. and Ord, K., 1994. Kendall‘s Advanced Theory of Statistics, Volume 1, Sixth edition, Edward Arnold, London.Google Scholar
  17. Thas, O., Rayner, J.C.W., 2005. Smooth tests for the zero inflated Poisson distribution. Biometrics 61 (3), 808–815.MathSciNetCrossRefGoogle Scholar
  18. Thas, O., Rayner, J.C.W., Best, D.J., 2007. Smooth tests for the logistic distribution. Submitted.Google Scholar
  19. Thas, O., Rayner, J.C.W., De Boeck, B., 2007. Generalised Emerson recurrence relations. In preparation.MATHGoogle Scholar

Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  1. 1.School of Mathematical and Physical SciencesUniversity of NewcastleAustralia
  2. 2.Department of Applied Mathematics, Biometrics and Process ControlGhent UniversityGentBelgium

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