A comparison of uniformity tests



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Marhuenda García, Yolanda and Morales González, Domingo and Pardo Llorente, María del Carmen (2005) A comparison of uniformity tests. Statistics: A Journal of Theoretical and Applied Statistics, 39 (4). pp. 315-328. ISSN 0233-1888

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Problems of goodness-of-fit to a given distribution can usually be reduced to test uniformity. The uniform distribution appears due to natural random events or due to the application of methods for transforming samples from any other distribution to the samples with values uniformily distributed in the interval (0,1), Thus, one can solve the problem of testing if a sample comes from a given distribution by testing whether its transformed sample is distributed according to the uniform distribution. For this reason, the methods of testing for goodness-of-fit to a uniform distribution have been widely investigated. In this paper, a comparative power analysis of a selected set of statistics is performed in order to give suggestions on which one to use for testing uniformity against the families of alternatives proposed by Stephens [Stephens, M.A., 1974, EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730-737.]. Definition and some relevant features of the considered test statistics are given in section 1. Implemented numerical processes to calculate percentage points of every considered statistic are described in section 2. Finally, a Monte Carlo simulation experiment has been carried out to fulfill the mentioned target of this paper.

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This work was supported by the grants BMF2003-00892, BMF2003-04820 and GV04B/670. The authors thank the referees for their comments and proposals leading to a better and more complete revised version.

Uncontrolled Keywords:Uniformity tests; Monte carlo simulation; Power; Inefficiency
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:17504
Deposited On:20 Dec 2012 11:05
Last Modified:25 Jul 2018 10:50

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