Some Comments on the EDF Statistics of Goodness-of-Fit Tests

The test of goodness-of-fit is an important means to establish a statistical model. Many test statistics reach their own extreme value at an "ideal sample" but EDF statistics not. It certainly affects the power of the tests. In present paper, we propose some adjusted EDF statistics which have this property in order to improve EDF tests. Monte Carlo simulations show that the adjusted EDF statistics are more powerful than EDF ones in many cases, especially for heavy tail alternative distributions. We also consider the relations between the behavior of the tests and their extreme value points.