For the purpose of measuring inequality or concentration, the Theil Index (also entropy index) is defined as the sum product of relative values of the distribution, times the natural logarithm of the same values.
More precisely, if we have n values summing up to a total value of
where each fraction is defined as
then the Theil index is defined as
Issues and Challenges
Open Source implementations of the Theil index are available in
- the Python library Concentration Library