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I am working with copula-based models. Copula models allow to models the margins separately from the dependencies structures. However, non-copula models do not allow for such separation.

My question is,

since the non-copula models do not allow for separation of the margins from dependencies structure, then, how we can estimate the margins? I meant we only have a joint distribution function which contains the information of margins and dependencies. So, how we can assume that the margins are, for example, Gaussians, while we do not have a specific function for them.

Maryam
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    If you have the joint then you have everything that you can wish for. The copulas is for the case when you don't have the joint. The main purpose of copulas is not to separate the marginals from dependency, but it is to construct the joint when you have only marginals. – Aksakal Jul 30 '18 at 18:06
  • @Aksakal does univariate gaussian margins implies that the dependency is Gaussian as well? – Maryam Jul 30 '18 at 18:26
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    No: see https://stats.stackexchange.com/questions/30159. – whuber Jul 30 '18 at 18:28
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    No, and it's easy to see why intuitively. You yourself wrote that copula decouple dependency from marginals. So, logically you can plug the Gaussian marginal into any copula and get some kind of a joint distribution. – Aksakal Jul 30 '18 at 18:38

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