  We introduce a new discrepancy score between two distributions that gives an
indication on their similarity. While much research has been done to determine
if two samples come from exactly the same distribution, much less research
considered the problem of determining if two finite samples come from similar
distributions. The new score gives an intuitive interpretation of similarity;
it optimally perturbs the distributions so that they best fit each other. The
score is defined between distributions, and can be efficiently estimated from
samples. We provide convergence bounds of the estimated score, and develop
hypothesis testing procedures that test if two data sets come from similar
distributions. The statistical power of this procedures is presented in
simulations. We also compare the score's capacity to detect similarity with
that of other known measures on real data.
