On Fourier-Based Inequality Indices.

Area of Science:

• Economics
• Applied Mathematics
• Data Analysis

Background:

• Inequality indices quantify economic disparities, typically ranging from 0 (complete equality) to 1.
• Traditional indices were developed to measure wealth heterogeneity.
• Existing measures may lack novel analytical approaches for certain characteristics.

Purpose of the Study:

• Introduce a new inequality index based on Fourier transform principles.
• Explore the potential applications of this novel index.
• Demonstrate the utility of Fourier transforms in analyzing established inequality measures.

Main Methods:

• Development of a new inequality index leveraging Fourier transform properties.
• Application of Fourier transform techniques to existing inequality metrics, including Gini and Pietra indices.
• Comparative analysis of the novel index against traditional measures.

Main Results:

• The proposed Fourier transform-based inequality index exhibits unique and promising characteristics.
• Established inequality indices, such as Gini and Pietra, can be effectively represented using Fourier transforms.
• This approach provides a novel and simplified method for illuminating the properties of inequality measures.

Conclusions:

• Fourier transform offers a powerful new framework for inequality analysis.
• The novel index and the re-formulation of existing indices provide enhanced tools for economic disparity research.
• This methodology opens avenues for new applications in quantitative economics and data science.