A method to obtain new copulas from a given one. (English) Zbl 1079.62056

Morillas, Patricia Mariela

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.

MSC:

62H05

Characterization and structure theory for multivariate probability distributions; copulas

Keywords:

given marginals; Archimedean copulas; mixtures