For two independently drawn samples from continuous distributions,
a statistical test based on the mutual information statistic is proposed
for the null hypothesis that both the samples originate from the same
population. Asymptotic properties of the test statistic under the null
hypothesis of equality is developed. It is demonstrated through simulation
that this test is more powerful than the commonly used nonparametric
tests in many situations. As an application we discuss the information
leak of e-passports. Using the mutual information based test, we detect
information leak in a situation where other non-parametric tests fail.