Measuring multidimensional inequality: a new proposal based on the Fourier transform
CoRR(2024)
摘要
Inequality measures are quantitative measures that take values in the unit
interval, with a zero value characterizing perfect equality. Although
originally proposed to measure economic inequalities, they can be applied to
several other situations, in which one is interested in the mutual variability
between a set of observations, rather than in their deviations from the mean.
While unidimensional measures of inequality, such as the Gini index, are widely
known and employed, multidimensional measures, such as Lorenz Zonoids, are
difficult to interpret and computationally expensive and, for these reasons,
are not much well known. To overcome the problem, in this paper we propose a
new scaling invariant multidimensional inequality index, based on the Fourier
transform, which exhibits a number of interesting properties, and whose
application to the multidimensional case is rather straightforward to calculate
and interpret.
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