A new nonparametric test for two sample problem based on order statistics is suggested. This test can be successful in the case of small samples. The probabilities of the statistic are given. Comparisons with KolmogorovSmirnov, Mann Whitney-Wilcoxon, and Wilks’ empty block test for small sample sizes are made by the simulation.

We shall prove the equivalence bewteen the convergences of Mann and implicit Mann iterations dealing with various classes of non-Lipschitzian operators.