Trying to model a variable using a three parameter weibull distribution

So I am trying to build a regression to model a variable whose distribution happens to coincide well with a 3 parameter weibull distribution. Given how x—a multi variate term—is in both a both a power and an exponential, how would I be able to describe the effect of whatever intercepts I arrive at for my x values? Is there a different distribution that might be easier to create an explainable model?