It seems that lognormal and Burr distributions are the best to fit my data. Can I compare their goodness of fit using a Kolmogorov-Smirnov test? The lognormal has 2 parameters whereas Burr has 3. To compare the values of the KS test, must the distributions have the same number of parameters?
The Kolmogorov-Smirnov test finds the maximum difference between the CDFs of the two distributions (or ECDFs, if you're using empirical data rather than distributions) so using the Kolmogorov-Smirnov test should be no problem for you.