On the Gini Mean Difference Arc-Lengths Test for Circular Data
نویسندگان
چکیده
In this paper, we propose a new test of uniformity on the circle based on the Gini mean difference of the sample arc-lengths, i.e. the gaps between successive observations on the circumference of the circle. These sample arc-lengths are analogous to sample spacings, which are the gaps between successive observations on the real line. Such a Gini mean difference test is analogous to Rao’s spacings test, which has been used to test the uniformity of circular data. We obtain both the exact and asymptotic distributions of the Gini mean difference arc-lengths test, 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. Some examples of circular data analysis are also considered. It is also seen that the Gini mean difference arc-lengths tests is more asymptotically efficient than Rao’s test in the sense of Pitman asymptotic relative efficiency.
منابع مشابه
On the Gini Mean Difference Test for Circular Data
In this paper, we propose a new test of uniformity on the circle based on the Gini mean difference of the sample arc-lengths. These sample arc-lengths, which are the gaps between successive observations on the circumference of the circle, are analogous to sample spacings on the real line. The Gini mean difference, which compares these arc-lengths between themselves, is analogous to Rao’s spacin...
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