Morillas, Patricia Mariela A method to obtain new copulas from a given one. (English) Zbl 1079.62056 Metrika 61, No. 2, 169-184 (2005). Summary: Given a strictly increasing continuous function \(\varphi\) from \([0,1]\) to \([0,1]\) and its pseudo-inverse \(\varphi^{[-1]}\), conditions that \(\varphi\) must satisfy for \(C_\varphi(x_1,\dots,x_n)= \varphi^{[-1]}(C(\varphi (x_1),\dots,\varphi(x_n)))\) to be a copula for any copula \(C\) are studied. Some basic properties of the copulas obtained in this way are analyzed and several examples of generator functions \(\varphi\) that can be used to construct copulas \(C_\varphi\) are presented. In this manner, a method to obtain from a given copula \(C\) a variety of new copulas is provided. This method generalizes that used to construct Archimedean copulas in which the original copula \(C\) is the product copula, and it is related with mixtures. Cited in 3 ReviewsCited in 44 Documents MSC: 62H05 Characterization and structure theory for multivariate probability distributions; copulas Keywords:given marginals; Archimedean copulas; mixtures PDF BibTeX XML Cite \textit{P. M. Morillas}, Metrika 61, No. 2, 169--184 (2005; Zbl 1079.62056) Full Text: DOI OpenURL