2025/11/30 by Asim Ghosh, Bikas K. Chakrabarti, Ghosh, Asim +1 · 1 citation
#physics.soc-ph
paper · pdf · doi:10.48550/arxiv.2512.00754
We study relations between three inequality indices, namely the Gini (g), Pietra (p) and Kolkata (k) introduced in 1912, 1915 and 2014 respectively and all are derived from the Lorenz function L(x) introduced in 1905. The Kolkata index (which corresponds to a fixed point of the complementary Lorenz function Lc(x) ≡ 1-L(x)) gives the fraction k of wealth possessed by the richest 1-k fraction of people (k = 0.8 corresponds to Pareto's 80-20 law from 1896). We show rigorously that while the Pietra index value p should be greater than or equal to 2k-1, the Robin Hood index should strictly be equal to the excess wealth fraction 2k-1 possessed by the richest 1-k fraction of people. Our numerical data analysis for US IRS Income data (1983-2022), Bollywood (India) movie income data (1999-2024) and the citation inequalities across the publications by forty Nobel Laureates (2020-2025) in Economics, Physics, Chemistry and Medicine clearly show that p/(2k-1) is always greater than unity but the deviation is never more than five percent. Assuming some simple analytic form for the Lorenz function, we also derived the relations k = (1/2) + (3/8)g for small g values and p/g = 3/4. However, by considering the Lorenz function appropriate for the generalized Pareto power law distribution, we obtain an extended range (1+ < p/g ≤ e/2) that captures most of the empirical data.