Theilindeksen

Theilindeksen, or Theil indices, are a family of statistical measures used to quantify inequality in a distribution, most commonly of income or expenditure. They were introduced by Dutch economist Henri Theil in the 1960s as part of the generalized entropy class of inequality measures. The Theil index is based on concepts from information theory and treats inequality as a deviation from perfect equality. In a population of N units with incomes y_i and average income μ, the Theil T index is commonly defined as T = (1/N) ∑ (y_i / μ) ln (y_i / μ). It is nonnegative and equals zero when all units have equal income; it reaches its maximum of ln N in the case of perfect concentration of income.

Theil indices also include Theil L, a related form that belongs to the same generalized entropy family and is based on the reciprocal relation to income shares. The Theil indices are valued for their decomposability: the overall inequality can be additively decomposed into within-group and between-group components, allowing researchers to assess how much of inequality arises within groups (such as regions, sectors, or demographic groups) and how much from differences between groups.

Applications of Theilindeksen span economics and social sciences, where they are used to measure income and wealth distribution, analyze changes over time, and study disparities in areas such as energy consumption or health outcomes. Potential limitations include sensitivity to extreme values, the requirement for positive values in some variants, and interpretation that depends on population size and context.