Hey salohcin.

You might want to consider using a non-linear general regression model where you specify the distributions of each variable and its constraints.

In SAS there is a procedure called NLMIXED that does this and there are also MCMC techniques.

I'd suggest taking a look at NLMIXED if you can (in SAS) and see if you can specify all of the constraints explicitly so that you can get estimates for the regression co-efficients given both models (along with standard errors).