Theil Index

From Open Risk Manual

Definition

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.

Details

More precisely, if we have n values E_i summing up to a total value of


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

where each fraction is defined as


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

then the Theil index is defined as


T = \sum^{n}_{i=1} w_{i} \ln{w_{i}}

Usage

None

Variations

None

Issues and Challenges

None

Implementations

Open Source implementations of the Theil index are available in

See Also

References