Abstract
We introduce and study a class of bivariate copulas depending on two univariate functions which generalizes the well-known Archimedean family. We provide several examples and some results about the concordance order.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alsina C., Frank, M.J., Schweizer, B. (2006). Associative functions: triangular norms and copulas. Singapore: World Scientific (to appear)
Amblard C., Girard S. (2002). Symmetry and dependence properties within a semiparametric family of bivariate copulas. Journal of Nonparametric Statistics 14:715–727
Avérous J., Dortet-Bernadet J.L. (2004). Dependence for Archimedean copulas and aging properties of their generating functions. Sankhyā: The Indian Journal of Statistics 66:1–14
Capéraà P., Fougères A.L., Genest C. (2000). Bivariate distributions with given extreme value attractor. Journal of Multivariate Analysis 72:30–49
Cuadras C.M., Augé J. (1981). A continuous general multivariate distribution and its properties. Communications in Statistics A - Theory and Methods 10:339–353
De Schuymer, B., De Meyer, H., De Baets, B. (2005). On some forms of cycle-transitivity and their relation to commutative copulas. In: Proceedings of EUSFLAT–LFA Conference, Barcelona, pp. 178–182.
Durante, F. (2005). A new class of symmetric bivariate copulas, Preprint n.19, Dipartimento di Matematica E. De Giorgi, Lecce.
Durante F., Mesiar R., Sempi C. (2006). On a family of copulas constructed from the diagonal section. Soft Computing 10:490–494 DOI 10.1007/s00500-005-0523-7
Frees E.W., Valdez E.A. (1998). Understanding relationships using copulas. North American Actuarial Journal 2:1–25
Genest C., MacKay J. (1986). Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. Canadian Journal of Statistics 14:145–159
Genest C., Rivest L.-P. (1993). Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 55:698–707
Hennessy D.A., Lapan H.E. (2002). The use of Archimedean copulas to model portfolio allocations. Mathematical Finance 12:143–154
Joe H. (1997). Multivariate models and dependence concepts. Chapman & Hall, London
Klement E.P., Mesiar R., Pap E. (2000). Triangular norms. Kluwer, Dordrecht
Marshall A., Olkin I. (1979). Inequalities: Theory of majorization and its applications. Academic, New York
Müller A., Scarsini M. (2005). Archimedean copulæ and positive dependence. Journal of Multivariate Analysis 93:434–445
Nelsen R.B. (1999). An introduction to copulas. Springer, Berlin Heidelberg New York
Rodríguez-Lallena J.A., Úbeda-Flores M. (2004). A new class of bivariate copulas. Statistics and Probability Letters 66:315–325
Salvadori, G., De Michele, C. (2004). Frequency analysis via copulas: Theoretical aspects and applications to hydrological events. Water Resources Research 40, DOI: 10.1029/2004WR003133.
Schweizer B., Sklar A. (1983). Probabilistic metric spaces. North Holland, New York
Sklar A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris 8:229–231
Sklar A. (1973). Random variables, bivariate distribution functions and copulas. Kybernetika 9:449–460
Wang W., Wells M.T. (2000). Model selection and semiparametric inference for bivariate failure-time data. Journal of the American Statistical Association 95:62–76
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Durante, F., Quesada-Molina, J.J. & Sempi, C. A Generalization of the Archimedean Class of Bivariate Copulas. AISM 59, 487–498 (2007). https://doi.org/10.1007/s10463-006-0061-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10463-006-0061-9