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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."
The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance). [2] It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order to transform one input string into another.
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.
In computational linguistics and computer science, edit distance is a string metric, i.e. a way of quantifying how dissimilar two strings (e.g., words) are to one another, that is measured by counting the minimum number of operations required to transform one string into the other.
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 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).