Copula function works only with uniform margins. However, using maximum likelihood estimation method or any other method to estimate the copula parameters, we need to specify the margins of each variables. For example,

$C(u_1, u_2) = F(F_1(x_1), F_2(x_2))$

Then, the loglikelihood function would be like this:

$L(\theta) = \sum log c(F_1(x_1,\theta_1),F_2(x_2,\theta_2);\theta)$

Where $\theta$ is copula parameter need to maximized. $\theta_1$ and $\theta_2$ are the parameters of the margins. So, why do we need to have the parameters of the margins inside copula while copula only works with uniform margins.


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