1. How to measure multidimensional variation?
- Author
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Auricchio, Gennaro, Giudici, Paolo, and Toscani, Giuseppe
- Subjects
Mathematics - Statistics Theory ,62H20, 62H99 - Abstract
The coefficient of variation, which measures the variability of a distribution from its mean, is not uniquely defined in the multidimensional case, and so is the multidimensional Gini index, which measures the inequality of a distribution in terms of the mean differences among its observations. In this paper, we connect these two notions of sparsity, and propose a multidimensional coefficient of variation based on a multidimensional Gini index. We demonstrate that the proposed coefficient possesses the properties of the univariate coefficient of variation. We also show its connection with the Voinov-Nikulin coefficient of variation, and compare it with the other multivariate coefficients available in the literature., Comment: 23 pages, 4 figures more...
- Published
- 2024