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Measuring social inequality with quantitative methodology: Analytical estimates and empirical data analysis by Gini and k indices

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  • Inoue, Jun-ichi
  • Ghosh, Asim
  • Chatterjee, Arnab
  • Chakrabarti, Bikas K.

Abstract

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.

Suggested Citation

  • Inoue, Jun-ichi & Ghosh, Asim & Chatterjee, Arnab & Chakrabarti, Bikas K., 2015. "Measuring social inequality with quantitative methodology: Analytical estimates and empirical data analysis by Gini and k indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 184-204.
    • Handle: RePEc:eee:phsmap:v:429:y:2015:i:c:p:184-204
    DOI: 10.1016/j.physa.2015.01.082
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    References listed on IDEAS

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    1. Ghosh, Asim & Chatterjee, Arnab & Inoue, Jun-ichi & Chakrabarti, Bikas K., 2016. "Inequality measures in kinetic exchange models of wealth distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 465-474.
    2. Palestini, Arsen & Pignataro, Giuseppe, 2016. "A graph-based approach to inequality assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 65-78.
    3. Chatterjee, Arnab & Chakrabarti, Anindya S. & Ghosh, Asim & Chakraborti, Anirban & Nandi, Tushar K., 2016. "Invariant features of spatial inequality in consumption: The case of India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 169-181.
    4. Remuzgo, Lorena & Trueba, Carmen & Sarabia, José María, 2016. "Evolution of the global inequality in greenhouse gases emissions using multidimensional generalized entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 146-157.
    5. Chatterjee, Arnab & Ghosh, Asim & Chakrabarti, Bikas K., 2017. "Socio-economic inequality: Relationship between Gini and Kolkata indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 583-595.
    6. Barrio, Rafael A. & Govezensky, Tzipe & Ruiz-Gutiérrez, Élfego & Kaski, Kimmo K., 2017. "Modelling trading networks and the role of trust," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 68-79.

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