Characterizations of the uniform distribution via sample spacings and nonlinear transformations

✍ Scribed by Anand Paul

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 71 KB
• Volume: 284
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1016/s0022-247x(03)00355-x

✦ Synopsis

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.