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The Theil index is a statistic primarily used to measure economic inequality [1] and other economic phenomena, though it has also been used to measure racial segregation. [2] [3] The Theil index T T is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy.
A third "symmetrized" Theil index (Theil-S) is the arithmetic average of the two previous indices. The formula of the third Theil index has some similarity with the Hoover index (as explained in the related articles). As in case of the Hoover index, the symmetrized Theil index does not change when swapping the incomes with the income earners.
The formula for general entropy for real values of ... For example, GE(0) is the mean log deviation a.k.a. Theil L index, GE(1) is the Theil T index, ...
The price index for some period is usually normalized to be 1 or 100, and that period is called "base period." A Törnqvist or Törnqvist-Theil price index is the weighted geometric mean of the price relatives using arithmetic averages of the value shares in the two periods as weights. [1]
The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
Here the Theil-T index is applied. The inverse value yielded by this function has a concrete meaning as well. There are several possible incomes to which a Euro may belong, which is randomly picked from the sum of all unequally distributed incomes. This welfare function marks the income, which a randomly selected Euro most likely belongs to.
The Atkinson index is defined in reference to a corresponding social welfare function, where mean income multiplied by one minus the Atkinson index gives the welfare equivalent equally distributed income. Thus the Atkinson index gives the share of current income which could be sacrificed, without reducing social welfare, if perfect inequality ...
As defined by Theil (1950), the Theil–Sen estimator of a set of two-dimensional points (x i, y i) is the median m of the slopes (y j − y i)/(x j − x i) determined by all pairs of sample points. Sen (1968) extended this definition to handle the case in which two data points have the same x coordinate.