I'm interested in your problem. Please, give me a simple example as to understand the details. As a first step, I would infere the support for U and V. For a, 0<=U<=1 and 0<Z<Inf. Then, I would construct the marginal for U and V. At last, construct f(u,v). But, I don't exactly know how.
Do you have any web page were the issue is discussed?