TY - JOUR

T1 - Measuring social inequality with quantitative methodology

T2 - Analytical estimates and empirical data analysis by Gini and k indices

AU - Inoue, Jun-ichi

AU - Ghosh, Asim

AU - Chatterjee, Arnab

AU - Chakrabarti, Bikas K.

PY - 2015/7/1

Y1 - 2015/7/1

N2 - Social inequality manifested across different strata of human existence can be quantified in several ways. Here we compute non-entropic measures of inequality such as Lorenz curve, Gini index and the recently introduced k index analytically from known distribution functions. We characterize the distribution functions of different quantities such as votes, journal citations, city size, etc. with suitable fits, compute their inequality measures and compare with the analytical results. A single analytic function is often not sufficient to fit the entire range of the probability distribution of the empirical data, and fit better to two distinct functions with a single crossover point. Here we provide general formulas to calculate these inequality measures for the above cases. We attempt to specify the crossover point by minimizing the gap between empirical and analytical evaluations of measures. Regarding the k index as an 'extra dimension', both the lower and upper bounds of the Gini index are obtained as a function of the k index. This type of inequality relations among inequality indices might help us to check the validity of empirical and analytical evaluations of those indices. (C) 2015 Elsevier B.V. All rights reserved.

AB - Social inequality manifested across different strata of human existence can be quantified in several ways. Here we compute non-entropic measures of inequality such as Lorenz curve, Gini index and the recently introduced k index analytically from known distribution functions. We characterize the distribution functions of different quantities such as votes, journal citations, city size, etc. with suitable fits, compute their inequality measures and compare with the analytical results. A single analytic function is often not sufficient to fit the entire range of the probability distribution of the empirical data, and fit better to two distinct functions with a single crossover point. Here we provide general formulas to calculate these inequality measures for the above cases. We attempt to specify the crossover point by minimizing the gap between empirical and analytical evaluations of measures. Regarding the k index as an 'extra dimension', both the lower and upper bounds of the Gini index are obtained as a function of the k index. This type of inequality relations among inequality indices might help us to check the validity of empirical and analytical evaluations of those indices. (C) 2015 Elsevier B.V. All rights reserved.

KW - Social inequality

KW - Gini and k-indices

KW - Empirical data analysis

KW - Mixtures of distributions

KW - SCIENCE

KW - WEALTH

KW - INCOME

U2 - 10.1016/j.physa.2015.01.082

DO - 10.1016/j.physa.2015.01.082

M3 - Article

VL - 429

SP - 184

EP - 204

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -