How to find the statistical distribution that best fits with some noise measurements?

I have some non Gaussian noise measurements and I want to find a statistical model that best represents those measurements.

The statistical models that I used for comparison are Middleton Class A , Alpha stable and the normal Gaussian distributions.

First I calculated the PDF and the CCDF of the measurements and of each one the models.

Then I compared the models with the measurements by calculating the Kull-Back Libeler divergence and by calculating the MSE between the PDF of measures and those of the statistical models.

I also calculated the power spectral density (PSD) of measurements the PSD of the noise resulting from each one the models.

Do you know other methods or metrics to do such comparison?

Thanks.