# Theil-Index

The Theil index was developed by the econometrician Henri Theil and is used for statistical description of income and wealth distributions.

## Definition

For persons with income is the average income and are defined in the Convention as follows Theil Indices:

MLD stands for mean log deviation. Apply to the relationships

## Relations / derivations

Claude Shannon developed his entropy measure of the probability of occurrence of an event. Part derived its index from it. The Theil index can be understood as the probability of a population of removed from a euro comes from one particular individual. This is the same as the first term: the share in total income of an individual.

Is that Shannon's measure, it shall

.

Is a Gleichverteilungsmaß, with corresponding Ungleichverteilungsmaß.

## Decomposability

The Theil index aggregates the weighted sum of the inequality by subgroups. And so, that can be calculated from the difference of distributions in countries such as the unequal distribution in Germany.

If the population can be divided into sub-groups and the income share of a subset of the total income, then describes the unequal distribution in the sub-group and is the average income of the group. The Theil index is

.

Thus described, the Theil index is then the "contribution" of the subgroup to unequal distribution in the entire group.

A more popular measure is the Gini coefficient, but in the wealth and poverty reports from the Federal and the Theil index is used besides the Gini coefficient. The Gini coefficient is not as separable as the Theil coefficient.