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