comparing 4 different signals

I have some noise measurements and 4 different models that can generate a similar noises using estimated parameters from the real measurements. To compare the estimated noises I calculated the PDF, the CCDF and the PSD.

To compare the results I used the Kull-Back Leibler divergence of the PDF, the MSE of the CCDF and the RMSE and the corr2 matlab function for the PSD.

I am not sure if I did the right thing.

Can you please tell me if what I did is correct and do you know any other way or function to make such comparison?

Thanks.

Are you wanting to measuring total noise power or noise density?

Actually I am more interested to the measuring of the noise density.
The measurements show that the noise is non-Gaussian: it is very Height and it have two components : a Gaussian and with some pulses and the PDF is heavy tailed.
Also if a pulse happens it is followed by resulting damped oscillations (other successive pulses with decreasing power).
What I am looking for is to know how to prove that those damped oscillation are correlated.

I found two statistical models (Middleton Class A and Alpha Stable) that are able to create impulsive noises and every body is using them. The problem is that those models suppose that the pulses are i.i.d and non correlated witch is not true in my case.

I found an other model that is able to create impulsive noise with correlated pulses and I want to use it. But first I have to justify why I chosen this model.
That is why I tried to compare it with the measurements and with the resulting noises from the other models.

It's PSD is the most similar to the PSD of the measurements but the PSD of the other models are plat.
For the PDF and CDF the results are close to the measurements but the other models gives better results.

Do you think that I am in the right way ??