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.

翻译：经典检验方法已可用于分布函数一致性的两样本检验。其中，Kolmogorov-Smirnov检验（柯尔莫戈洛夫-斯米诺夫检验）还能以不同形式提供检验结果的图形化解释。本文提出了对Kolmogorov-Smirnov检验的改进方案，以提升其统计功效。所提出的新检验基于所谓的全局包络检验（global envelope test），该检验与Kolmogorov-Smirnov检验类似，同样支持图形化解释。本检验基于秩统计量，且适用于$n \geq 2$个样本的比较。通过广泛的模拟研究，我们对两样本情况下的备择假设进行了比较，并讨论了其解释方法。最后，我们将所提出的方法应用于实际数据：具体而言，比较了不同年龄段男孩与女孩的身高分布，以及不同花卉物种的萼片长度分布。