Comparing probability distributions

Chart: Probability distribution functions for daily returns of S&P500, WIG20, NatGas, Gold and EURUSD

data from 2011-01-10 do 2012-03-19

We are going back to the subject of similarities of return characteristics of various assets.

I was looking for a way to compare various probability distributions and decide which ones are the most similar to each other.

I've found three methods that can be of help here:

• Kolmogorov-Smirnov distance
• Cramer-von Mises criterion
• Kullback-Leibler distance

Since results given by these methods return vary depending on the type of distributions we compare, deciding which of them and how to use requires further research.