Measuring social inequality with quantitative methodology: analytical estimates and empirical data analysis by Gini and indices
arXiv:1406.2874 · doi:10.1016/j.physa.2015.01.082
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 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 index as an `extra dimension', both the lower and upper bounds of the Gini index are obtained as a function of the index. This type of inequality relations among inequality indices might help us to check the validity of empirical and analytical evaluations of those indices.
22 pages, 7 figs, 2 tables
References in corpus (7)
- Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States
- Colloquium: Statistical mechanics of money, wealth, and income
- Evidence for the exponential distribution of income in the USA
- Inequality in Societies, Academic Institutions and Science Journals: Gini and k-indices
- Global inequality in energy consumption from 1980 to 2010
- The distribution of first-passage times and durations in FOREX and future markets
- Fluctuations in time intervals of financial data from the view point of the Gini index
Cited by in corpus (8)
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- Success of Social Inequality Measures in Predicting Critical or Failure Points in Some Models of Physical Systems
- Modelling Trading Networks and the Role of Trust
- Econophysics Through Computation