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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 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 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.
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.
This is the same as the first term, the individual's share of aggregate income." is a bit of a problem. Theil's index is a redundancy (The gap between maximumn entropy and effective entropy), so it is in the entropy domain. The operation 1-exp(-Theil) turns it into an Atkinson index, which you can treat as a "probability".