A test for uniformity with unknown limits based on d'agostino's D

Abstract

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 Cramer-von Mises distance between the empirical distribution function and a rectangular distribution with suitably estimated endpoints. The limiting null distribution of D is found.D'Agostino's D test for uniformity with unknown limits U-statistics characterization of the uniform distribution