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require 'facets/math/approx_equal'
module Math
# Calculates the Gini Coefficient (a measure of inequality of a distribution
# based on the area between the Lorenz curve and the uniform curve).
#
# http://en.wikipedia.org/wiki/Gini_coefficient
#
# This is a slightly cleaner way of calculating the Gini Coefficient then
# the previous implementationj.
#
# GC = \frac{\sum_{i=1}^N (2i-N-1)x_i}{N^2-\bar{x}}
#
def self.gini_coefficient(array)
return -1 if size <= 0 or any? { |x| x < 0 }
return 0 if size < 2 or all? { |x| approx_equal(x,0) }
s = 0
sort.each_with_index { |li,i| s += (2*i+1-size)*li }
s.to_f/(size**2*mean).to_f
end
## OLD WAY
## GC = \frac{1}{N} \left ( N+1-2\frac{\sum_{i=1}^N (N+1-i)y_i}{\sum_{i=1}^N y_i} \right )
## def self.gini_coefficient2(array)
## return -1 if size <= 0 or any? { |x| x < 0 }
## return 0 if size < 2 or all? { |x| Math::float_equal(x,0) }
## s = 0
## sort.each_with_index { |yi,i| s += (size - i)*yi }
## (size+1-2*(s.to_f/sum.to_f)).to_f/size.to_f
## end
end
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9 entries across 8 versions & 2 rubygems