For the purpose of measuring concentration, the Gini Index (also Gini coefficient) is an index defined in terms of the Lorentz curve of distribution values.
More precisely, if we have n values summing up to a total value of
and the fractional value is defined as
Then the Gini index is defined as the area under the Lorenz curve which is geometrically reduced to
Gini's absolute mean difference is defined as
The relative mean difference is defined as where
The Gini index is equivalently given by
Issues and Challenges
NB: Sometimes the formula appears also with the opposite sign!
Open Source implementations of the Gini index are available in