Hi Leila

Per se, there are no restrictions on parameter number when using the Kolmogorov-Smirnov non-parametric test to compare distribution functions. In particular, there is no requirement that the alternatives have the same number of parameters.

But for testing against a two-parameter distribution like the normal, Kolmogorov-Smirnov is not that powerful. I'd recommend the Shapiro-Wilk test in that case.

What is your objective, anyway? Most of the time I've had to think about empirical distributions, a simple histogram tells a lot. That can be enough?

Best

Marco