Application of The Theil Index
Theil's measure can be converted by the operation into one of the indexes of Anthony Barnes Atkinson, where may or may not be used to introduce an inequality aversion factor into the formula, with being the default. The result of the conversion also has been called normalized Theil index.
James E. Foster used such a measure to replace the Gini coefficient in Amartya Sen's welfare function W = f(income,inequality). The income e.g. is the average income for individuals in a group of income earners. Thus, Foster's welfare function can be computed directly from the Theil index, if the conversion is included into the computation of the average per capita welfare function:
Using the "Theil-L" index (see below) for in that formula yields results similar to using the Atkinson index for computing the welfare function.
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