Yes, you can use goodness of fit test such as the Kolmogorov-Smirnov test, the Anderson-Darling test, or a Chi-square test-. They are based in the comparison of the cumulative empirical distributions. As everyone has advantages and disadvantages depending on the data, usually they are combined in an Index to see the best fit.
Check this paper
Reynolds, K; R Jr.M; T. Burk, y H. Won-Chin,. 1988. Godness-of-fit tests and model selection procedures for diameter distribution model. For. Sci. 34 (2): 373-379.
hope this is useful
The short answer is yes but how you would make the comparison will depend on what you are trying to accomplish. Could you please give more details?
Thanks for replies. In fact, I have already results for goodness of fit tests of some recently generalized Weibull distribution but I am confused due to one point that Weibull is limiting case of BurrIII. So can we compare limiting case with generalize?
I think so. If you are comparing the fitting to empirical data, the general form and the special cases would give different values for the goodness of fit tests (i.e. the weibull would be a Burr form with less parameters). Also, different fitting methods would give different goodness of fit values. I asumme that by limiting case you mean a special case of the Burr III distribution, don.t you?
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