Hello everyone,


I recently became aware of the existence of the copula concept.
So, I have been reading a few things about copulas lately, but
I cannot seem to find information on the following question:


* Let's say that I have marginals for the random variables a,b,c,d.
* Is it possible to learn a copula from the 4 marginals p(a),p(b),p(c),p(d)
that allows me to derive then any marginal I might be interested in?


E.g. once I have obtained the copula c(a,b,c,d), can I calculate the marginal for (a,d)?


Thank you in advance!
N.



Copulas and marginals thereof
Answer is yes, it's Sklar's theorem.


The copula is merely a form of normalization that makes all your marginals U(0,1). Given a copula and the marginals, you can reconstruct the original distribution, and a fortiori get any marginal you're interested in. 


