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Calculating Gini Coefficients with GINICOEFF
This function is extremely efficient at calculating Gini coefficients on large data sets.
What are Gini Coefficients?
Gini Coefficients are a frequently-used method of measuring inequalities such as income distribution in a population.
A Gini Coefficient can be calculated as "the relative mean difference" - the mean of the difference between every possible pair of data points, divided by the mean of all the data points. A Gini Coefficient ranges from 0 (everyone has the same income) to 1 (one person has all the income).
Some Gini Income coefficients are:
Sweden 0.23
France 0.28
UK 0.34
USA 0.45
Brazil 0.57
Zimbabwe 0.57
(Source: http://en.wikipedia.org/wiki/List_of_countries_by_income_equality)
The Gini formula is often written as:
G=SUM(i=1 to n) SUM(j=1 to n) ABS(Data points(i)-Data points(j)) / (n*n*Average(Data points))
where Data points is the range of data and n is the number of points in Data points.
A Bias Correction factor of n/(n-1) is usually applied.
A more efficient formula has been developed by Angus Deaton (Princeton 1997):
G=(n+1)/(n-1)-2 /(n*(n-1)* Average(Data points))*SUM(i=1 to n) Data points(i)*Rank(i)
Where Rank is 1 for the largest value and n for the smallest value.
This formula has the bias correction factor built-in.
For more information on Gini Coefficients see:
http://en.wikipedia.org/wiki/Gini_coefficient or http://mathworld.wolfram.com/GINICOEFficient.html
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