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

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

Usage

None

Variations

None

Issues and Challenges

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

Implementations

Open Source implementations of the Gini index are available in

• the R package Ineq
• the Python library Concentration Library

See Also

• Hall-Tideman Index