Abstract
Inequality indices are quantitative scores that gauge the divergence of wealth distributions in human societies from the "ground state" of pure communism. While inequality indices were devised for socioeconomic applications, they are effectively applicable in the context of general non-negative size distributions such as count, length, area, volume, mass, energy, and duration. Inequality indices are commonly based on the notion of Lorenz curves, which implicitly assume the existence of finite means. Consequently, Lorenz-based inequality indices are excluded from the realm of infinite-mean size distributions. In this paper we present an inequality index that is based on an altogether alternative Langevin approach. The Langevin-based inequality index is introduced, explored, and applied to a wide range of non-negative size distributions with both finite and infinite means.
Highlights
This paper is written in honor of the 60th birthday of Professor Yurij Holovatch
Following the pioneering work of Vilfredo Pareto on the distribution of wealth in human societies [7], the study of socioeconomic inequality became a major topic in economics and in the social sciences, as well as a major topic of wide public debate [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]
Inequality indices measure the divergence of wealth distributions from the “ground state” of pure communism, and score this divergence
Summary
This paper is written in honor of the 60th birthday of Professor Yurij Holovatch. The scientific interests of Professor Holovatch span from statistical physics to econophysics and sociophysics. I. Eliazar from the Langevin equation in the setting of U-shaped potential landscapes [66], we introduce and explore a novel scenario-based inequality index that is applicable for a wide range of non-negative size distributions with both finite and infinite means. In [41, 42] it was demonstrated how the socioeconomic methods of Lorenz curves and inequality indices can be “imported” to the physical sciences, and serve there to quantify the statistical heterogeneity of general non-negative size distributions with finite means. This paper moves in the opposite direction, and demonstrates how a Langevin-based approach can effectively replace the Lorenz-based approach of gauging inequality This is yet another example of the importance of the trans-disciplinary flow of ideas between different fields of science. We describe the general application of the scenario-based equality index as a gauge of inequality (section 7), and conclude with illustrative examples of the application (section 8)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
