Proving the characterization of Archimedean copulas via Dini derivatives
Kybernetika, Tome 52 (2016) no. 5, pp. 785-790 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this note we prove the characterization of the class of Archimedean copulas by using Dini derivatives.
In this note we prove the characterization of the class of Archimedean copulas by using Dini derivatives.
DOI : 10.14736/kyb-2016-5-0785
Classification : 60E05, 62E10
Keywords: Archimedean copula; derived number; Dini derivative
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Fernández-Sánchez, Juan; Úbeda-Flores, Manuel. Proving the characterization of Archimedean copulas via Dini derivatives. Kybernetika, Tome 52 (2016) no. 5, pp. 785-790. doi: 10.14736/kyb-2016-5-0785

[1] Alsina, C., Frank, M. J., Schweizer, B.: Associative Functions: Triangular Norms and Copulas. World Scientific, Singapore 2006. | DOI | MR | Zbl

[2] Amo, E. de, Carrillo, M. Díaz, Sánchez, J. Fernández: Characterization of all copulas associated with non-continuous random variables. Fuzzy Sets Syst. 191 (2012), 103-112. | DOI | MR

[3] Berg, L., Krüppel, M.: De Rahm's singular function and related functions. Z. Anal. Anw. 19 (2000), 227-237. | DOI | MR

[4] Cherubini, U., Luciano, E., Vecchiato, W.: Copula Methods in Finance. Wiley Finance Series, John Wiley and Sons Ltd., Chichester 2004. | DOI | MR | Zbl

[5] Durante, F., Jaworski, P.: A new characterization of bivariate copulas. Comm. Statist. Theory Methods 39 (2010), 2901-2912. | DOI | MR | Zbl

[6] Durante, F., Sempi, C.: Principles of Copula Theory. Chapman and Hall/CRC, London 2015. | DOI | MR

[7] Genest, C., MacKay, J.: Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. Canad. J. Statist. 14 (1986), 145-159. | DOI | MR | Zbl

[8] Hagood, J. W., Thomson, B. S.: Recovering a function from a Dini derivative. Amer. Math. Monthly 113 (2006), 34-46. | DOI | MR | Zbl

[9] Jaworski, P., Durante, F., Härdle, W., (editors), T. Rychlik: Copula Theory and its Applications. Lecture Notes in Statistics-Proceedings, Springer, Berlin-Heidelberg 2010. | DOI | MR

[10] Ling, C. H.: Representation of associative functions. Publ. Math. Debrecen 12 (1965), 189-212. | MR | Zbl

[11] Łojasiewicz, S.: An Introduction to the Theory of Real Functions. Third Edition. A Wiley-Interscience Publication, John Wiley and Sons Ltd., Chichester 1988. | MR

[12] McNeil, A. J., Nešlehová, J.: Multivariate Archimedean copulas, $d$-monotone functions and $l_1$-norm symmetric distributions. Ann. Stat. 37 (2009), 3059-3097. | DOI | MR

[13] McNeil, A. J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton 2005. | MR | Zbl

[14] Natanson, L. P.: Theory of Functions of a Real Variable. Vol. I, revised edition. Frederick Ungar Publishing, New York 1961. | MR

[15] Nelsen, R. B.: An Introduction to Copulas. Second Edition. Springer, New York 2006. | DOI | MR

[16] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, New York 1983. Reprinted, Dover, Mineola NY, 2005. | MR | Zbl

[17] Sklar, A.: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231. | MR

[18] Wysocki, W.: Characterizations of Archimedean n-copulas. Kybernetika 51 (2015), 212-230. | DOI | MR | Zbl

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