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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.
In statistics, the uncertainty coefficient, also called proficiency, entropy coefficient or Theil's U, is a measure of nominal association. It was first introduced by Henri Theil [ citation needed ] and is based on the concept of information entropy .
For the Theil index also the term "Theil entropy" had been used. This caused confusion. As an example, Amartya Sen commented on the Theil index, "given the association of doom with entropy in the context of thermodynamics, it may take a little time to get used to entropy as a good thing."
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 data used are prices and quantities in two time-periods, (t-1) and (t), for each of n goods which are indexed by i.
The generalized entropy index has been proposed as a measure of income inequality in a population. [1] It is derived from information theory as a measure of redundancy in data. In information theory a measure of redundancy can be interpreted as non-randomness or data compression ; thus this interpretation also applies to this index.
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.
The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...
The Atkinson index is defined as: (, …,) = {(=) / (=) / = (,...,) = +where is individual income (i = 1, 2, ..., N) and is the mean income.. In other words, the Atkinson index is the complement to 1 of the ratio of the Hölder generalized mean of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the geometric mean).