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I am quite new to copula models. The main idea of the copula is based on the Sklar's theorem. In copula models, we first need to transform the data to copula data (standard uniform [0,1]). Then, we can apply our model to estimates the model parameters. After that, we need to back to the original data using inverse cumulative distribution function. My question is, why do we need the last step while we already have our original data?

For example,

this question

Also, Sklar's theorem stated that.

$C(u_1, u_2) = F(F_1^{(-1)} (u_1), F_2^{(-1)} (u_2))$

Maryam
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    It depends on what you're trying to achieve. Can you supply a quote -- with the relevant context -- which says to do this, and then it will be easier to explain what's going on in that situation. – Glen_b May 15 '18 at 05:24
  • @Glen_b Thank you so much for your kind comment. It is from Sklar's theorem. Also, I read some question here. I will provide the link. – Maryam May 15 '18 at 05:47
  • [Sklar's theorem](http://mathworld.wolfram.com/SklarsTheorem.html) doesn't seem to say you must do anything. Where does the 'must' arise? – Glen_b May 15 '18 at 06:59

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