Customizing Generalizations of the Kolmogorov-Smirnov Goodness-of-fit Test

This paper presents a method of customizing goodness-of-fit tests that transforms the empirical distribution function in such a way as to create tests for certain alternatives. Using the @ , g transform described in Blom(1958), one can create non-parametric tests for an assortment of alternative distributions. As examples, three new ( f , g )-corrected Kolmogorov-Smirnov tests for goodness-of-fit are discussed. One of these tests is powerful for testing whether or not the data come from an alternative that is heavier in the tails. Another test identifies whether or not the data come from an alternative which is heavier in the middle of the distribution. The last test identifies if the data come from an alternative in which the first or third quartile is far from the corresponding quartile of the hypothesized distribution. The behavior of the three new tests is investigated through a power study.

Keywords:

• Goodness-of-fit Tests
• δ-Corrected Kolmogorov-Smirnov Test