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Keywords:
Archimedean copula; derived number; Dini derivative
Summary:
In this note we prove the characterization of the class of Archimedean copulas by using Dini derivatives.
References:
[1] Alsina, C., Frank, M. J., Schweizer, B.: Associative Functions: Triangular Norms and Copulas. World Scientific, Singapore 2006. DOI 10.1142/9789812774200 | MR 2222258 | Zbl 1100.39023
[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 10.1016/j.fss.2011.10.005 | MR 2874826
[3] Berg, L., Krüppel, M.: De Rahm's singular function and related functions. Z. Anal. Anw. 19 (2000), 227-237. DOI 10.4171/zaa/947 | MR 1748045
[4] Cherubini, U., Luciano, E., Vecchiato, W.: Copula Methods in Finance. Wiley Finance Series, John Wiley and Sons Ltd., Chichester 2004. DOI 10.1002/9781118673331 | MR 2250804 | Zbl 1163.62081
[5] Durante, F., Jaworski, P.: A new characterization of bivariate copulas. Comm. Statist. Theory Methods 39 (2010), 2901-2912. DOI 10.1080/03610920903151459 | MR 2755533 | Zbl 1203.62101
[6] Durante, F., Sempi, C.: Principles of Copula Theory. Chapman and Hall/CRC, London 2015. DOI 10.1201/b18674 | MR 3443023
[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 10.2307/3314660 | MR 0849869 | Zbl 0605.62049
[8] Hagood, J. W., Thomson, B. S.: Recovering a function from a Dini derivative. Amer. Math. Monthly 113 (2006), 34-46. DOI 10.2307/27641835 | MR 2202919 | Zbl 1132.26321
[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 10.1007/978-3-642-12465-5 | MR 3075361
[10] Ling, C. H.: Representation of associative functions. Publ. Math. Debrecen 12 (1965), 189-212. MR 0190575 | Zbl 0137.26401
[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 0952856
[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 10.1214/07-aos556 | MR 2541455
[13] McNeil, A. J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton 2005. MR 2175089 | Zbl 1347.00025
[14] Natanson, L. P.: Theory of Functions of a Real Variable. Vol. I, revised edition. Frederick Ungar Publishing, New York 1961. MR 0148805
[15] Nelsen, R. B.: An Introduction to Copulas. Second Edition. Springer, New York 2006. DOI 10.1007/0-387-28678-0 | MR 2197664
[16] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, New York 1983. Reprinted, Dover, Mineola NY, 2005. MR 0790314 | Zbl 0546.60010
[17] Sklar, A.: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231. MR 0125600
[18] Wysocki, W.: Characterizations of Archimedean n-copulas. Kybernetika 51 (2015), 212-230. DOI 10.14736/kyb-2015-2-0212 | MR 3350557 | Zbl 1340.62054
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