Characterizations of the uniform distribution via sample spacings and nonlinear transformations

We prove that an absolutely continuous probability distribution with compact support is uniformly distributed if and only if the mean sample spacings resulting from a random sample of size N are all equal for every integer N. We also present a related characterization of uniformity using nonlinear transformations.We discuss potential applications of these results to hypothesis testing and to testing the effectiveness of different random number generators.  2003 Elsevier Inc. All rights reserved.