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ArticleOriginal scientific text

Title

Goodness-of-fit tests based on characterizations of continuous distributions

Authors 1, 2

Affiliations

  1. Department of Statistics, University of Adelaide, North Tce, Adelaide, South Australia, 5001
  2. Institute of Mathematics, Maria Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Abstract

We construct goodness-of-fit tests for continuous distributions using their characterizations in terms of moments of order statistics and moments of record values. Our approach is based on characterizations presented in [2]-[4], [5], [9].

Keywords

ENG
uniform, Weibull, exponential, Pareto distributions, significance probability, k-record values, goodness-of-fit tests, order statistics, characterization of distributions

Bibliography

  1. W. Dziubdziela and B. Kopociński, Limiting properties of the k-th record values, Zastos. Mat. 15 (1976), 187-190.
  2. Z. Grudzień and D. Szynal, Characterization of continuous distributions in terms of moments of extremal statistics, J. Math. Sci. 81 (1996), 2912-2936.
  3. Z. Grudzień and D. Szynal, Characterizations of continuous distributions via moments of the k-th record values with random indices, Brandenburgische Technische Universität Cottbus, Fakultät für Mathematik, Naturwissenschaften und Informatik, Reihe Mathematik, M-05/1997 (1997).
  4. Z. Grudzień and D. Szynal, Characterizations of continuous distributions via moments of record values, J. Appl. Statist. Sci. 9 (2000), 93-104.
  5. G. D. Lin, Characterizations of continuous distributions via expected values of two functions of order statistics, Sankhyā Ser. A 52 (1990), 84-90.
  6. K. Morris and D. Szynal, A goodness-of-fit test for the uniform distribution based on a characterization, in: XX Internat. Sympos. on Stability Problems for Stochastic Models (Lublin-Nałęczów, 1999), Abstracts, p. 119, submitted to J. Math. Sci.
  7. P. Pawlas and D. Szynal, Relations for single and product moments of k-th record values from exponential and Gumbel distributions, J. Appl. Statist. Sci. 7 (1998), 53-62.
  8. P. Pawlas and D. Szynal, Recurrence relations for single and product moments of k-th record values from Weibull distributions, and a characterization, ibid. 10 (2000), 17-26.
  9. Y. H. Too and G. D. Lin, Characterizations of uniform and exponential distributions, Statist. Probab. Lett. 7 (1989), 357-359.
  10. S. S. Wilks, Mathematical Statistics, Wiley, New York, 1962.
Applicationes Mathematicae
2000/27/4
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Pages:
475-488
Main language of publication
English
Received
2000-02-07
Accepted
2000-06-02
Published
2000
Exact and natural sciences