Some notes on biasedness and unbiasedness of two-sample Kolmogorov-Smirnov test

This paper deals with two-sample Kolmogorov-Smirnov test and its biasedness. This test is not unbiased in general in case of different sample sizes. We found out most biased distribution for some values of significance level $\alpha$. Moreover we discovered that there exists number of observation and significance level $\alpha$ such that this test is unbiased at level $\alpha$.