The probability weighted characteristic function and goodness-of-fit testing

We introduce the notion of the probability weighted characteristic function (PWCF) as a generalization of the characteristic function. Some of the properties of the PWCF and of its empirical counterpart are studied and the potential use of these quantities in goodness-of-fit testing is examined in detail. The corresponding limiting null distributions and consistency results for location-scale models are derived and finite-sample comparisons are presented. Also, the notion of the PWCF is extended to arbitrary dimension.