# Can I compare goodness of fit using the Kolmogrov-Smirnov test, if the distributions have a different number of parameters?

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?

• I have tried to edit the question to correct a few minor grammatical things but mostly to make the title more closely reflect the intent of the question. If you don't like my changes, feel free to revert them. – Silverfish Jun 4 '16 at 3:34

• 1. If the test is being used (rather than merely comparing test statistics), the parameters are being estimated from the data, so this wouldn't be a Kolmogorov-Smirnov test, it would be a form of Lilliefors test - and no longer nonparametric. $\;$ 2. If we're just comparing KS-statistics, and if the three parameter Burr is flexible enough to approximate the lognormal fairly well, it will essentially always fit at least as well as the lognormal, since it will also be free to not approximate the lognormal ... ctd – Glen_b May 19 '16 at 22:31