Fitting a copula vs. directly fitting a multivariate distribution I understand that the joint density of two random variables $f(x,y)$ can be decomposed as the product of its marginals and a copula: $f(x,y) = g(x)k(y) \times c(G(x),K(y))$. Alternatively this may be written using CDFs as $F(x,y) = C(G(x),K(y))$.
Is it possible to directly estimate the joint density $f(x,y)$ or the joint distribution $F(x,y)$ without estimating the copula? What are the benefits/costs of obtaining the joint density by first estimating the marginals and copula instead?

It is possible to estimate the joint distribution without using copulas. If you know joint distribution, $f(x,y; \Theta) $ up to an unknown parameter vector, $\Theta$, you shouldn't use a copula.
Copulas are useful when you know there is dependence between random variables, but you don't know a joint distribution that can describe this dependence. Say, $g(x) = Gamma(\alpha, \beta)$ and $k(y) = Lognormal(\mu, \sigma)$. There is no closed-form expression for $f(x,y)$.  In this case, you can use a copula to estimate the joint distribution from the marginals.
