We investigate the properties of a new transformation of copulas based on the co-copula and an univariate function. It is shown that several families in the copula literature can be interpreted as particular outputs of this transformation. Symmetry, association, ordering and dependence properties of the resulting copula are established.
If the inline PDF is not rendering correctly, you can download the PDF file here.
 Amblard, C. and S. Girard (2009). A new extension of bivariate FGM copulas. Metrika 70(1), 1-17.
 Blomqvist, N. (1950). On a measure of dependence between two random variables. Ann. Math. Statist. 21(4), 593-600.
 Bruckner, A.M. and E. Ostrow (1962). Some function classes related to the class of convex functions. Pacific J. Math 12(4), 1203-1215.
 Di Bernardino, E. and D. Rullière (2013). On certain transformations of Archimedean copulas: Application to the nonparametric estimation of their generators. Depend. Model. 1, 1-36.
 Dolati, A. and M. Úbeda-Flores (2009). Constructing copulas by means of pairs of order statistics. Kybernetika 45(6), 992-1002.
 Durante, F. (2006). A new class of symmetric bivariate copulas. J. Nonparametr. Stat. 18(7-8), 499-510.
 Durante, F., J. Fernández-Sánchez, and W. Trutschnig (2014). Solution to an open problem about a transformation on the space of copulas. Depend. Model. 2, 65-72.
 Durante, F., R. Foschi, and P. Sarkoci (2010). Distorted copulas: constructions and tail dependence. Comm. Statist. Theory Methods 39(12), 2288-2301.
 Durante, F., S. Girard, and G. Mazo (2015). Copulas based on Marshall-Olkin machinery. In U. Cherubini, F. Durante, and S. Mulinacci (Eds.), Marshall-Olkin Distributions - Advances in Theory and Applications, pp. 15-31. Springer, Cham.
 Durante, F., S. Girard, and G. Mazo (2016). Marshall-Olkin type copulas generated by a global shock. J. Comput. Appl. Math. 296, 638-648.
 Durante, F. and C. Sempi (2016). Principles of Copula Theory. CRC Press, Boca Raton FL.
 Genest, C., J. Nešlehovà, and N. B. Ghorbal (2010). Spearman’s footrule and Gini’s gamma: a review with complements. J. Nonparametr. Stat. 22(8), 937-954.
 Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall, London.
 Klement, E. P., R. Mesiar, and E. Pap (2005). Transformations of copulas. Kybernetika 41(4), 425-434.
 Manstavicius, M. and G. Bagdonas (2019). A class of bivariate copula mappings. Fuzzy Sets Syst., 354(1), 48-62.
 Michiels, F. and A. De Schepper (2012). How to improve the fit of Archimedean copulas by means of transforms. Stat. Papers 53(2), 345-355.
 Morillas, P. M. (2005). A method to obtain new copulas from a given one. Metrika 61(2), 169-184.
 Nelsen, R. B. (2006). An Introduction to Copulas. Second edition. Springer, New York.
 Schweizer, B. and E. F. Wolff (1981). On nonparametric measures of dependence for random variables. Ann. Statist. 9(4), 879-885.
 Valdez, E. A. and Y. Xiao (2011). On the distortion of a copula and its margins. Scand. Actuar. J. 2011(4), 292-317.
 Zhang, M.-H. (2008). Modelling total tail dependence along diagonals. Insurance Math. Econom. 42(1), 73-80.
Dependence Modeling aims to provide a medium for exchanging results and ideas in the area of multivariate dependence modeling. Topics include Copula methods, environmental sciences, estimation and goodness-of-fit tests, extreme-value theory, limit laws, mass transportations, measures of association, multivariate distributions and tests, quantitative risk management, risk assessment, risk models, risk measures and stochastic orders and time series.