How to properly parametrise underlying distribution

Hi.

I am trying to build a model that takes as an input six distribution functions f_{i}(x). The model is complex and highly non-linear, most of it was not build by me. All I can do is to treat it only as a "black box" that takes input parameterised by me and produces output that can be compared to some data points. Assuming that model is right I am trying to tune parameters of the input distributions. My question is the following:

How can I verify whether parameterisation of f_{i} (x) is chosen wisely?

I can imagine that if I give some more freedom in some regions of x, fit has a potential to perform better. But then obviously too much freedom causes convergence problems. Is there a theory that is relevant for my problem that I could study?

Thank you for your help,

peg