2008 Volume 38 Issue 3 Pages 505-515
In the Kolmogorov-Smirnov theorem, the underlying distribution is assumed to be a continuous distribution. On the other hand, real data in practice is always given in a discretized (rounded) form. In this paper we establish a Donsker type theorem in the fashion of the modern empirical process theory to obtain a (right) Kolmogorov-Smirnov test for discretized data.