Title:
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On quasi-homogeneous copulas (English) |
Author:
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Mayor, Gaspar |
Author:
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Mesiar, Radko |
Author:
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Torrens, Joan |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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44 |
Issue:
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6 |
Year:
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2008 |
Pages:
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745-756 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given. (English) |
Keyword:
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copula |
Keyword:
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diagonal section |
Keyword:
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quasi-homogeneity |
MSC:
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62E10 |
MSC:
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62H05 |
idZBL:
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Zbl 1196.62058 |
idMR:
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MR2488902 |
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Date available:
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2009-09-24T20:39:53Z |
Last updated:
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2013-09-21 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/135888 |
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Reference:
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[1] Aczél J.: Lectures on Functional Equations and Their Applications (Math.Sci. Engrg., Vol. 19). Academic Press, New York 1966 MR 0208210 |
Reference:
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[2] Alsina C., Frank M. J., Schweizer B.: Associative Functions.Triangular Norms and Copulas. World Scientific Publishing, Singapore 2006 Zbl 1100.39023, MR 2222258 |
Reference:
|
[3] Bertino S.: Sulla dissomiglianza tra mutabili cicliche.Metron 35 (1977), 53–88 Zbl 0437.62026 |
Reference:
|
[4] Baets B. De, Meyer, H. De, Mesiar R.: Asymmetric semilinear copulas.Kybernetika 43 (2007), 221–233 Zbl 1136.62350, MR 2343397 |
Reference:
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[5] Durante F., Kolesárová A., Mesiar, R., Sempi C.: Copulas with given diagonal sections: Novel constructions and applications.Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 15 (2007), 397–410 Zbl 1158.62324, MR 2362234, 10.1142/S0218488507004753 |
Reference:
|
[6] Durante F., Kolesárová A., Mesiar, R., Sempi C.: Semilinear copulas.Fuzzy Sets and Systems 159 (2008), 63–76 MR 2371303 |
Reference:
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[7] Durante F., Mesiar, R., Sempi C.: On a family of copulas constructed from the diagonal section.Soft Computing 10 (2006), 490–494 Zbl 1098.60016, 10.1007/s00500-005-0523-7 |
Reference:
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[8] Durante F., Sempi C.: Semicopulae.Kybernetika 41 (2005), 315–328 MR 2181421 |
Reference:
|
[9] Ebanks B. R.: Quasi-homogeneous associative functions.Internat. J. Math. Math. Sci. 21 (1998), 351–358 Zbl 0899.39003, MR 1609715, 10.1155/S0161171298000489 |
Reference:
|
[10] Fredricks G. A., Nelsen R. B.: Copulas constructed from diagonal sections.In: Distributions with Given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1977, pp. 129–136 MR 1614666 |
Reference:
|
[11] Fredricks G. A., Nelsen R. B.: The Bertino family of copulas.In: Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena, eds.), Kluwer, Dordrecht 2002, pp. 81–91 Zbl 1135.62334, MR 2058982 |
Reference:
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[12] Genest C., Molina J. J. Quesada, Lallena J. A. Rodríguez, Sempi C.: A characterization of quasi-copulas.J. Multivariate Anal. 69 (1999), 193–205 MR 1703371, 10.1006/jmva.1998.1809 |
Reference:
|
[13] Klement E. P., Kolesárová A.: Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators.Kybernetika 41 (2005), 329–348 MR 2181422 |
Reference:
|
[14] Klement E. P., Mesiar, R., Pap E.: Triangular Norms.Kluwer Academic Publishers, Dordrecht 2000 Zbl 1087.20041, MR 1790096 |
Reference:
|
[15] Nelsen R. B.: An Introduction to Copulas.Second edition (Springer Series in Statistics). Springer-Verlag, New York 2006 Zbl 1152.62030, MR 2197664 |
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