Foster–Greer–Thorbecke indices
The Foster–Greer–Thorbecke indices are a family of poverty metrics. The most commonly used index from the family, "FGT", puts higher weight on the poverty of the poorest individuals, making it a combined measure of poverty and income inequality and a popular choice within development economics. The indices were introduced in a 1984 paper by economists Erik Thorbecke, Joel Greer, and James Foster. The individual indices within the family are derived by substituting different values of the parameter "α" into the following equation: formula_1 where "z" is the poverty threshold," N" is the number of  people in the economy, "H" is the number of poor (those with incomes at or below "z"), "y" is the income of each individual "i. "If formula_2 is low then the FGT metric weights all the individuals with incomes below z roughly the same. The higher the value of "α, "the greater the weight place on the poorest individuals. The higher the FGT statistic, the more poverty there is in an economy. FGTand FGT. With "α "= 0, the formula reduces to the headcount ratio: the fraction of the population that lives below the poverty line. formula_3 With "α "=  1, the formula reduces to the poverty gap index. formula_4 The "FGT" can be rewritten as: formula_5 , where formula_6 is the average income of the poor. Thus, the "FGT" can be expressed as the product of the "FGT" and the average income gap of the poor. FGT. While the two reduced indexes are widely used, the most common FGT-specific index in development economics is the "α" = 2 version, which is the lowest (whole) parameter to weigh income inequality along with poverty. formula_7 The "FGT" can be rewritten as: formula_8 where "C" is the coefficient of variation among the  incomes of the poor, "H" is the total number of the poor, and "μ" is given by: formula_9. Other decompositions of the index are also possible. The only measure that combines "FGT", "FGT", and the Gini index is the Sen index. In Mexico, this version of the index was used to allocate federal government funds between regions for educational, health, and nutritional programs benefiting the poor. In 2010, the Government of Mexico adopted a multidimensional poverty measure based on a variant of the FGT measure that is to be used in targeting the allocation of social funds to poor households  at the municipality level.