So I know how to use goodness of fit tests generally. For example if I wanted to check whether my data came from a Poisson distribution I would first estimate the parameter using MLE (so just the sample average) and then apply goodness of fit tests.
But what about for a distribution like student-t, where the degree of freedom parameter is typically an integer and the MLE doesn't have a closed form solution (I think).
So I would imagine I would have,say, 1000 observations. I think my first step would be generating an estimate for the degree of freedom parameter (using MLE) and then be on my way doing the goodness of fit tests.
Please feel free to comment on this approach or what you would do differently.