Gini coefficient

The Gini coefficient is a measure of inequality developed by the Italian statistician Corrado Gini and published in his 1912 paper "Variabilità e mutabilità". It is usually used to measure income inequality, but can be used to measure any form of uneven distribution. The Gini coefficient is a number between 0 and 1, where 0 corresponds with perfect equality (where everyone has the same income) and 1 corresponds with perfect inequality (where one person has all the income, and everyone else has zero income). The Gini index is the Gini coefficient expressed in percentage form, and is equal to the Gini coefficient multiplied by 100.

Calculation

The small sample variance properties of G are not known, and large sample approximations to the variance of G are poor. In order for G to be an unbiased estimate of the true population value, it should be multiplied by n/(n-1).

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The Gini coefficient is calculated as a ratio of the areas on the Lorenz curve diagram. If the area between the line of perfect equality and Lorenz curve is A, and the area underneath the Lorenz curve is B, then the Gini coefficient is A/(A+B). This ratio is expressed as a percentage or as the numerical equivalent of that percentage, which is always a number between 0 and 1.

Related Topics:
Ratio - Lorenz curve

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The Gini coefficient is often calculated with the more practical Brown Formula shown below:

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G = | 1 - sum_{k=1}^{k=n} (X_{k} - X_{k-1}) (Y_{k} + Y_{k-1}) |

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G: Gini coefficient

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X: cumulated proportion of the population variable

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Y: cumulated proportion of the income variable

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