I am trying to better understand why some models are "covariance based" vs. why some other models are "correlation based".

1) For example, a Multivariate Normal Distribution calculates the covariances between different variables:

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2) Whereas a Copula Model "quantifies" the correlation between variables:

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  • Does anyone know why this is?
  • Why does a Multivariate Normal Distribution use Covariances but a Gaussian Copula use Correlation?

My guess is that Copulas are can be created using different probability distributions, and it might not be possible to calculate the covariances between data that is assumed to have come from different probability distributions - whereas it might be possible to calculate the corrleations?

  • $\begingroup$ @ Archana David : Is my reasoning correct? $\endgroup$
    – stats555
    Nov 23 at 5:52

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