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

• Autorzy: Kerwin Morris , Dominik Szynal
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2000
• Tom: 27
• Numer: 4
• Strony: 475-488

Daty

wydano

2000

otrzymano

2000-02-07

poprawiono

2000-06-02

Twórcy

autor

Kerwin Morris

• Department of Statistics, University of Adelaide, North Tce, Adelaide, South Australia, 5001

autor

Dominik Szynal

• Institute of Mathematics, Maria Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

• [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.