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].
@article{bwmeta1.element.bwnjournal-article-zmv27i4p475bwm,
author = {Kerwin Morris and Dominik Szynal},
title = {Goodness-of-fit tests based on characterizations of continuous distributions},
journal = {Applicationes Mathematicae},
volume = {27},
year = {2000},
pages = {475-488},
zbl = {1051.62510},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv27i4p475bwm}
}
Morris, Kerwin; Szynal, Dominik. Goodness-of-fit tests based on characterizations of continuous distributions. Applicationes Mathematicae, Tome 27 (2000) pp. 475-488. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i4p475bwm/
[000] [1] W. Dziubdziela and B. Kopociński, Limiting properties of the -th record values, Zastos. Mat. 15 (1976), 187-190. | Zbl 0337.60023
[001] [2] Z. Grudzień and D. Szynal, Characterization of continuous distributions in terms of moments of extremal statistics, J. Math. Sci. 81 (1996), 2912-2936. | Zbl 0871.62016
[002] [3] Z. Grudzień and D. Szynal, Characterizations of continuous distributions via moments of the -th record values with random indices, Brandenburgische Technische Universität Cottbus, Fakultät für Mathematik, Naturwissenschaften und Informatik, Reihe Mathematik, M-05/1997 (1997).
[003] [4] Z. Grudzień and D. Szynal, Characterizations of continuous distributions via moments of record values, J. Appl. Statist. Sci. 9 (2000), 93-104.
[004] [5] G. D. Lin, Characterizations of continuous distributions via expected values of two functions of order statistics, Sankhyā Ser. A 52 (1990), 84-90. | Zbl 0717.62010
[005] [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. | Zbl 1104.62317
[006] [7] P. Pawlas and D. Szynal, Relations for single and product moments of -th record values from exponential and Gumbel distributions, J. Appl. Statist. Sci. 7 (1998), 53-62. | Zbl 0901.62023
[007] [8] P. Pawlas and D. Szynal, Recurrence relations for single and product moments of -th record values from Weibull distributions, and a characterization, ibid. 10 (2000), 17-26. | Zbl 0961.62009
[008] [9] Y. H. Too and G. D. Lin, Characterizations of uniform and exponential distributions, Statist. Probab. Lett. 7 (1989), 357-359. | Zbl 0666.62010
[009] [10] S. S. Wilks, Mathematical Statistics, Wiley, New York, 1962. | Zbl 0173.45805