# Gini Index

## Definition

For the purpose of measuring name, sector or geographic concentration, the Gini Index (also Gini coefficient) is an index defined in terms of the Lorentz curve of the exposures.

## Details

More precisely, if we have n exposures $E_i$ summing up to a total exposure of

$E_T = \sum^{n}_{i=1} E_{i}$

and the fractional exposures $w_i$ are defined as

$w_{i} = \frac{E_i}{E_T}$

Then the Gini index is defined as the area under the Lorenz curve which is geometrically reduced to

$G = 1 + \frac{1}{n} \sum^{n}_{i=1} (1 - 2 i) w_{i}$

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## Issues and Challenges

NB: Sometimes the formula appears also with the opposite sign!

## Implementations

Open Source implementations of the Gini index are available in

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