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Sungur, Engin A.; Yang, Yimin

Diagonal copulas of Archimedean class. (English) Zbl 0900.62339

Commun. Stat., Theory Methods 25, No. 7, 1659-1676 (1996).
Summary: The concept of diagonal copulas is introduced and its properties are examined. It is shown that for the Archimedean class, the diagonal copula uniquely determines the corresponding copula. This fact helps to reduce the dimension and makes it easier to understand the underlying dependence structure without losing any information. Therefore diagonal copulas can be used in various stages of dependence model building, selection, fitting and diagnostics. In this paper we consider some of the possibilities on estimation, test of hypotheses and graphical data analysis.

Cited in 1 Review
Cited in 12 Documents

MSC:

62H99 Multivariate analysis
62-07 Data analysis (statistics) (MSC2010)

Keywords:

archimedean copulas; copulas; diagonal copulas
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\textit{E. A. Sungur} and \textit{Y. Yang}, Commun. Stat., Theory Methods 25, No. 7, 1659--1676 (1996; Zbl 0900.62339)
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References:

[1] DOI: 10.1080/03610928008827893 · Zbl 0449.62011
[2] Cook R.D., J. R. Statistical Soc., Series B 43 pp 210– (1981)
[3] DOI: 10.1007/BF01836543 · Zbl 0308.39009
[4] Frechet M., Annales de Universite de Lyon, Section A, Series 3 14 pp 53– (1951)
[5] Gaenssler P., Seminar on Empirical Processes (1987)
[6] DOI: 10.2307/3314660 · Zbl 0605.62049
[7] DOI: 10.2307/2684602
[8] DOI: 10.1080/01621459.1993.10476372
[9] Hille E., Functional Analysis and Semi-group (1957)
[10] Johnson N.L., Distributions in Statistics: Continuous Multivariate Distributions (1972) · Zbl 0248.62021
[11] Kimeldorf G., Commun. Statist.: Theor. Meth 15 (11) pp 3277– (1975)
[12] Marshall A.W., Jour. of American Statistical Association 83 (403) pp 843– (1988)
[13] DOI: 10.1080/03610918708812585 · Zbl 0609.62072
[14] Scarsini M., Stochastica 8 pp 201– (1984)
[15] DOI: 10.1214/aos/1176345528 · Zbl 0468.62012
[16] Schweizer B., Probabilistic Metric spaces (1983) · Zbl 0546.60010
[17] Sklar A., Inst. Statist 8 pp 229– (1959)
[18] Sungur, A.E. and Tuncer, Y. The Use of Copulas to Generate New Multivariate Distributions The Frontiers of Statistical Computation, Simulation, and Modeling. Proceedings of the First International Conference on Statistical Computing. Edited by: Nelsen, P.R. pp.197–222. Columbus: Academic Science Press. Vol 1, No. 25 · Zbl 0786.62054
[19] DOI: 10.1080/03610919008812920 · Zbl 0850.62409
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