— Ch. 1 · Origins And Development —
Gini coefficient.
~4 min read · Ch. 1 of 5
In 1912, Italian statistician Corrado Gini published a paper titled Variabilità e mutabilità. This document introduced the concept that would eventually bear his name. He proposed using the difference between a hypothetical straight line of perfect equality and an actual line depicting people's incomes as a measure of inequality. The work built upon earlier research by American economist Max Lorenz. In 1914, Gini applied this simple mean difference to income and wealth inequality in a subsequent study. He presented what he called the concentration ratio, which evolved into today's standard Gini coefficient. A geometrical interpretation appeared in 1915 when Gaetano Pietra linked Gini's ratio to observed areas of concentration. This altered version became the most commonly used inequality index in the following years. The first official country-wide use occurred in Canada during the 1970s. Canadian data from 1976 through the late 1980s showed indices ranging from 0.303 down to 0.284.
Mathematical Foundations
The calculation relies on the Lorenz curve, which plots the proportion of total population against cumulative income earned. A line at 45 degrees represents perfect equality where every person earns the same amount. The coefficient equals the area marked A divided by the total area of A and B combined. If no negative incomes exist, the value ranges strictly from 0 for total equality to 1 for absolute inequality. An alternative approach defines the coefficient as half of the relative mean absolute difference. This method calculates the average absolute difference between all pairs of items in a population. When income follows a continuous probability density function, integration replaces simple summation. For an exponential distribution, the result remains constant at one-half regardless of scale parameters. Some functional forms allow explicit calculation using error functions or Gamma functions. A table of distributions shows that Dirac delta implies zero variation while uniform distribution yields approximately 0.33. Log-normal distributions with specific standard deviations produce values near 0.5. These mathematical tools allow researchers to quantify dispersion without relying solely on visual curves.