25 lines
627 B
Ruby
25 lines
627 B
Ruby
require 'facets/math/sum'
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require 'facets/math/mean'
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require 'facets/math/approx_equal'
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module Math
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# Calculates the Theil index (a statistic used to measure
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# economic inequality).
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#
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# TI = \sum_{i=1}^N \frac{x_i}{\sum_{j=1}^N x_j} ln \frac{x_i}{\bar{x}}
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#
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# http://en.wikipedia.org/wiki/Theil_index
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#
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def self.theil_index(array)
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return -1 if array.size <= 0 or any? { |x| x < 0 }
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return 0 if array.size < 2 or all? { |x| approx_equal(x, 0) }
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m = mean(array)
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s = sum(array).to_f
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inject(0) do |theil, xi|
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theil + ((xi > 0) ? (log(xi.to_f/m) * xi.to_f/s) : 0.0)
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end
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end
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end
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