I have some values with unknown joint distribution, but I am assuming that the marginal distributions are two-part Normal Mixtures. I am modelling the dependency between the distributions via vine-copulas and pairwise copula constructions.
What I want to do is simulate new values from these distributions, taking into consideration the dependency between them.
What I did:
- Estimated the parameters of the marginals using R (bayesmix)
- Used an empirical distribution function to get uniform values from the sample ones, so that I could construct the copula (I could also have used the estimated distributions for the transform)
- Constructed a vine copula and simulated values from it, meaning I now have uniform values for all variables (VineCopula package)
What I still need to do:
- Use the generated uniform values that possess the dependency information to get the actual values from the distribution. The problem here comes from the fact that I do not know the inverse CDF of the Normal Mixture and how to do this in R. If it was any of the standard distributions, for which I could calculate the inverse (or the inverse is already implemented), there would be no problem.
So my question is, how can I do this? Is there a way to do this?
I would prefer answers with both theory and R, but will be perfectly satisfied with either.