I have same data and I would like to choose a model for it. To start with I fit an exponential distribution and a gamma distribution. Now I wanted to do a simple likelihood ratio test . However, I am told that to do this properly the two models have to be nested (which they are) and the parameter space of one has to be in the interior of the other, not on the boundary. This second condition doesn't seem to hold unfortunately.
What can I do?