1007 Submissions

[2] viXra:1007.0034 [pdf] replaced on 2012-01-11 19:14:18

On the Gini Mean Difference Test for Circular Data

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 14 Pages.

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 spacings statistic, 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. Illustrative examples in circular data analysis are also given. It is shown that a generalized Gini mean difference test has better asymptotic efficiency than the corresponding generalized Rao's test in the sense of Pitman asymptotic relative efficiency.
Category: Statistics

[1] viXra:1007.0016 [pdf] submitted on 13 Mar 2010

Studies in Statistical Inference, Sampling Techniques and Demography

Authors: Rajesh Singh, Jayant Singh, Florentin Smarandache
Comments: 64 pages

This volume is a collection of five papers. Two chapters deal with problems in statistical inference, two with inferences in finite population, and one deals with demographic problem. The ideas included here will be useful for researchers doing works in these fields.
Category: Statistics