  Classical tests are available for the two-sample test of correspondence of
distribution functions. From these, the Kolmogorov-Smirnov test provides also
the graphical interpretation of the test results, in different forms. Here, we
propose modifications of the Kolmogorov-Smirnov test with higher power. The
proposed tests are based on the so-called global envelope test which allows for
graphical interpretation, similarly as the Kolmogorov-Smirnov test. The tests
are based on rank statistics and are suitable also for the comparison of $n$
samples, with $n \geq 2$. We compare the alternatives for the two-sample case
through an extensive simulation study and discuss their interpretation.
Finally, we apply the tests to real data. Specifically, we compare the height
distributions between boys and girls at different ages, as well as sepal length
distributions of different flower species using the proposed methodologies.
