# Measuring distance between two empirical distributions

This is similar to the question Measuring the "distance" between two multivariate distributions, except that I want to measure distance between two data sets. I can imagine simply computing the mean, standard deviation, and other summary statistics and then somehow aggregating the differences for each distribution, but that does not seem very theoretically sound.

I wonder if there is a generally accepted method for doing this measurement.

• duplicate of this question? – user603 Dec 3 '13 at 10:20

If you have a model and can identify sufficient statistics for it, then, by comparing the sufficient statistics of both samples you can assess how different the information contained in each sample is. If they are very close, then the associated [likelihood functions] (http://en.wikipedia.org/wiki/Likelihood_function) would be similar, and therefore the inferences on the corresponding parameters would be similar as well.