The Modified Kolmogorov-Smirnov One-Sample Test Statistic

Abstract

The Kolmogorov-Smirnov (K-S) statistic is a well known nonparametric test statistic used to solve goodness-of fit problems. However, a disadvantage of the K-S is its low power when the true distribution differs from the hypothesized distribution in the tails. Here, a new methodology is proposed in which a modified K-S statistic is obtained. The simulation results indicate that the modified K-S statistic is preferable when the sample size is large.