What kind of probability distribution features one can make use of in order to identify a specific pdf? I was thinking of using the moments of the distribution (mean,var,skewness and kurtosis) but I am not sure whether specific moments (or combination of them) identify specific pdf.
Edited : The problem is the following:
I would like to know which features do I need to extract from a pdf in order to use some ML techniques and train a model such that it may perform a pdf clustering, i.e. train a model such that it can be able to classify whether a new data set (random values) may be represented by a certain pdf or not. Basically, something similar to GOF tests but using some more sophisticated techniques ( if they exist ).