Journal of Mathematical Sciences

, Volume 191, Issue 4, pp 538–549 | Cite as

Goodness-of-fit tests via characterizations. general approach

  • K. W. Morris
  • D. Szynal

We construct goodness-of-fit tests via characterizations of continuous distribution functions in terms of moments of k-th record values. U-statistics are used to estimate the associated expectations.


Continuous Distribution Gumbel Distribution International Seminar Continuous Distribution Function Lower Record 
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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  1. 1.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publishing, New York (1972).MATHGoogle Scholar
  2. 2.
    M. Bieniek and D. Szynal, “Recurrence relations for distribution functions and moments of k-th record values,” J. Math. Sci., 111, No. 3, 3511–3519 (2002).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    W. Dziubdziela and B. Kopociski, “Limiting properties of the k-th record values,” Zastos. Mat., 5, No. 2, 187–190 (1976).Google Scholar
  4. 4.
    Z. Grudzień and D. Szynal, “On the expected values of k-th record values and associated characterizations of distributions,” Probab. Statist. Decision Theory, A, 119–127 (1985).Google Scholar
  5. 5.
    Z. Grudzień and D. Szynal, “Characterization of continuous distributions via moments of record values,” J. Appl. Statist. Sci., 9, No. 2, 93–104 (2000).MathSciNetMATHGoogle Scholar
  6. 6.
    E. R. Hansen, A Table of Series and Products, Prentice–Hall, Inc., Englewood Cliffs, New Jersey (1975).MATHGoogle Scholar
  7. 7.
    E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. With the Special Assistance of H. J. M. d’Abrera, Holden–Day Series in Probability and Statistics, Holden–Day, Inc., San Francisco, Calif. (1975).Google Scholar
  8. 8.
    G. D. Lin. “Characterizations of continuous distributions via expected values of two functions of order statistics,” Sankhyā, A, No. 52, 84–90 (1990).Google Scholar
  9. 9.
    I. Malinowska, K.W. Morris , and D. Szynal, “On dual characterizations of continuous distributions in terms of expected values of two functions of order statistics and record values,” J. Math. Sci., 121, No. 5, 2664–2673 (2004).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    K.W. Morris and D. Szynal, “Tests derived from characterizations in terms of moments of record values,” Appl. Math., 30, No. 1, 11–37 (2003).MathSciNetMATHGoogle Scholar
  11. 11.
    K.W. Morris and D. Szynal, “Goodness-of-fit tests using dual versions of characterizations via moments of order statistics,” J. Math. Sci., 122, No. 4, 3365–3383 (2004).MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    K.W. Morris and D. Szynal, “Test resulting from characterizations using record values,” J. Math. Sci., 131, No. 3, 5646–5656 (2005).MathSciNetCrossRefGoogle Scholar
  13. 13.
    V. B. Nevzorov, Records: Mathematical Theory, American Mathematical Society, Providence (2001).Google Scholar
  14. 14.
    P. Pawlas and D. Szynal, “Relations for single and product moments of k-th record values from exponential and Gumbel distributions,” J. Appl. Statist., 7, No. 1, 53–61 (1998).MathSciNetMATHGoogle Scholar
  15. 15.
    D. A. Pierce, “The asymptotic effect of substituting estimators for parameters in certain types of statistics,” Ann. Statist., 10, No. 2, 475–478 (1982).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of AdelaideNorth Tce, AdelaideSouth Australia
  2. 2.Institute of MathematicsMaria Curie–Skłodowska UniversityLublinPoland

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