A test for uniformity with unknown limits based on D'Agostinos $D$

Although still being recommended as a goodness-of-fit test for normality, we present some motivations to consider D'Agostino's statistic D for testing of uniformity on an unknown interval. As a matter of fact, D turns out to be a linear function of the Cramér-von Mises distance between the empirical distribution function and a rectangular distribution with suitably estimated endpoints. The limiting null distribution of D is found.