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Parametric copulas with marginals that are regressions

In Dependence Modeling with Copulas (Harry Joe) I'm struggling to interpret the meaning of a statement. In Chaper 5.1, it is stated: Parametric inference for copulas For dependence modeling with ...
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Are there families of known parametric copulas for non-standard marginal normal distributions?

I know that a family of Gaussian copulas generates a standard bivariate normal distribution if and only if the marginal ones are standard normal. This characterizes the Gaussian copulas, where I have ...
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