Data fitting, Maximum Likelihood Estimation

Hello all,

I am using standard statistical distributions in MATLAB e.g., Normal, Lognormal, Rayeligh, Weibull etc. (generated using rand()) and further the Maximum Likelihood Estimation to estimate the distribution parameters in each case. Further, I am using the Kolmogorov-Smirnov (K-S) test to select the best (known) distribution while comparing the empirical CDF with the estimated one in each case. This technique correctly detects most of the distributions with the maximum p value criterion, however the problem comes with Rayleigh distribution which is incorrectly detected to be either Webiull or Nakagami most of the times. Anyone knows about the possible pitfalls in this procedure for Rayleigh distribution? Thanks.

Best Regards, Rizwan