Characterizations of the uniform distribution via sample spacings and nonlinear transformations |
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Authors: | Anand Paul |
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Institution: | Department of Decision and Information Sciences, Warrington College of Business Administration, University of Florida, Gainesville, FL 32611-7169, USA |
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Abstract: | 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. |
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Keywords: | Probability distributions Hypothesis testing Sample spacings |
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