Kolmogorov-Smirnov (KS) tests rely on the convergence to zero of the KS-distance $d(F_n,G)$ in the one sample case, and of $d(F_n,G_m)$ in the two sample case. In each case the assumption (the null hypothesis) is that $F=G$, and so $d(F,G)=0$. In this paper we extend the Dvoretzky-Kiefer-Wolfowitz-Massart inequality to also apply to cases where $F \neq G$, i.e. when it is possible that $d(F,G) > 0$.

翻译：Kolmogorov-Smirnov（KS）检验依赖于单样本情形下KS距离$d(F_n,G)$与双样本情形下$d(F_n,G_m)$收敛于零的性质。在这两种情形中，其前提假设（零假设）均为$F=G$，故有$d(F,G)=0$。本文扩展了Dvoretzky-Kiefer-Wolfowitz-Massart不等式，使其同样适用于$F \neq G$的情形，即允许$d(F,G) > 0$的情况。