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

Kerwin Morris; Dominik Szynal

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 4, page 475-488
  • ISSN: 1233-7234

Abstract

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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].

How to cite

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Morris, Kerwin, and Szynal, Dominik. "Goodness-of-fit tests based on characterizations of continuous distributions." Applicationes Mathematicae 27.4 (2000): 475-488. <http://eudml.org/doc/219290>.

@article{Morris2000,
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].},
author = {Morris, Kerwin, Szynal, Dominik},
journal = {Applicationes Mathematicae},
keywords = {uniform, Weibull, exponential, Pareto distributions; significance probability; k-record values; goodness-of-fit tests; order statistics; characterization of distributions},
language = {eng},
number = {4},
pages = {475-488},
title = {Goodness-of-fit tests based on characterizations of continuous distributions},
url = {http://eudml.org/doc/219290},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Morris, Kerwin
AU - Szynal, Dominik
TI - Goodness-of-fit tests based on characterizations of continuous distributions
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 4
SP - 475
EP - 488
AB - 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].
LA - eng
KW - uniform, Weibull, exponential, Pareto distributions; significance probability; k-record values; goodness-of-fit tests; order statistics; characterization of distributions
UR - http://eudml.org/doc/219290
ER -

References

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  1. [1] W. Dziubdziela and B. Kopociński, Limiting properties of the k -th record values, Zastos. Mat. 15 (1976), 187-190. Zbl0337.60023
  2. [2] Z. Grudzień and D. Szynal, Characterization of continuous distributions in terms of moments of extremal statistics, J. Math. Sci. 81 (1996), 2912-2936. Zbl0871.62016
  3. [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. [4] Z. Grudzień and D. Szynal, Characterizations of continuous distributions via moments of record values, J. Appl. Statist. Sci. 9 (2000), 93-104. 
  5. [5] G. D. Lin, Characterizations of continuous distributions via expected values of two functions of order statistics, Sankhyā Ser. A 52 (1990), 84-90. Zbl0717.62010
  6. [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. Zbl1104.62317
  7. [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. Zbl0901.62023
  8. [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. Zbl0961.62009
  9. [9] Y. H. Too and G. D. Lin, Characterizations of uniform and exponential distributions, Statist. Probab. Lett. 7 (1989), 357-359. Zbl0666.62010
  10. [10] S. S. Wilks, Mathematical Statistics, Wiley, New York, 1962. Zbl0173.45805

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