# Creating a Distribution

Say I want to create a multivariate distribution that perhaps, as an example, looks something like this.

f(x1,x2,x3)=f1(x1)*f2(x2)*f3(x3)*InverseStandardNormal[F1(x1)]*...


Obviously the function I am working on doesn't quite look like this but I hope you get the picture. It is a multivariate joint distribution that relies on individual marginal distributions, cumulative distributions, as well as other scaling factors.

Well. What I have done so far is the first bit of it (with the product of marginals)

ProductDistribution[
]


**Edit: ** The formula I want to create is number 8 in this paper http://library.wolfram.com/infocenter/Conferences/4312/coleman.nb?file_id=3546

Here is my attempt so far:

    densities = ProductDistribution[BetaDistribution[\[Alpha]Vector[[1]], \[Beta]Vector[[1]]], BetaDistribution[\[Alpha]Vector[[2]], \[Beta]Vector[[2]]], BetaDistribution[\[Alpha]Vector[[3]], \[Beta]Vector[[3]]], BetaDistribution[\[Alpha]Vector[[4]], \[Beta]Vector[[4]]], BetaDistribution[\[Alpha]Vector[[5]], \[Beta]Vector[[5]]], BetaDistribution[\[Alpha]Vector[[6]], \[Beta]Vector[[6]]], BetaDistribution[\[Alpha]Vector[[7]], \[Beta]Vector[[7]]], BetaDistribution[\[Alpha]Vector[[8]], \[Beta]Vector[[8]]]];
c]], Quantile[NormalDistribution[0, 1],
d]],
Quantile[NormalDistribution[0, 1],
e]], Quantile[NormalDistribution[0, 1],
f]], Quantile[NormalDistribution[0, 1],
g]], Quantile[NormalDistribution[0, 1],