New goodness-of-fit tests based on empirical distribution function

Distributional assumptions are at the core of statistical methods. Goodness-of-fit test statistics are used to examine whether there is a difference between the sample distribution and the empirical distribution. Although there are large number of goodness-of-fit tests in the literature, the powers of these statistics are different in each study. The purpose of the study is to obtain new powerful goodness-of-fit tests based on the empirical distribution function by using Cressie-Read power divergence statistics. In this study, power divergences statistics are transformed in order to introduce new goodness-of-fit tests. Critical values, type I error rates and powers of tests are obtained by using Monte Carlo for several sample sizes. Several power comparisons are performed to show that the new tests are generally more powerful than the original ones for testing normality.