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On the Gini Mean Difference Test for Circular Data
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https://doi.org/10.1080/03610926.2011.601947Abstract
We introduce a new test of isotropy or uniformity on the circle, based on the Gini mean difference of the sample arc-lengths and obtain both the exact and asymptotic distributions under the null hypothesis of circular uniformity. We also provide a table of upper percentile values of the exact distribution for small to moderate sample sizes. Illustrative examples in circular data analysis are also given. It is shown that a "generalized" Gini mean difference test has better asymptotic efficiency than a corresponding " generalized" Rao's test in the sense of Pitman asymptotic relative efficiency. © 2013 Taylor & Francis Group, LLC.
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