83 lines
2.4 KiB
Ruby
83 lines
2.4 KiB
Ruby
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module Statistics
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module Distribution
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class TStudent
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attr_accessor :degrees_of_freedom
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attr_reader :mode
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def initialize(v)
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self.degrees_of_freedom = v
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@mode = 0
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end
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### Extracted from https://codeplea.com/incomplete-beta-function-c
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### This function is shared under zlib license and the author is Lewis Van Winkle
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def cumulative_function(value)
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upper = (value + Math.sqrt(value * value + degrees_of_freedom))
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lower = (2.0 * Math.sqrt(value * value + degrees_of_freedom))
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x = upper/lower
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alpha = degrees_of_freedom/2.0
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beta = degrees_of_freedom/2.0
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Math.incomplete_beta_function(x, alpha, beta)
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end
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def density_function(value)
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return if degrees_of_freedom <= 0
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upper = Math.gamma((degrees_of_freedom + 1)/2.0)
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lower = Math.sqrt(degrees_of_freedom * Math::PI) * Math.gamma(degrees_of_freedom/2.0)
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left = upper/lower
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right = (1 + ((value ** 2)/degrees_of_freedom.to_f)) ** -((degrees_of_freedom + 1)/2.0)
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left * right
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end
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def mean
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0 if degrees_of_freedom > 1
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end
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def variance
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if degrees_of_freedom > 1 && degrees_of_freedom <= 2
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Float::INFINITY
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elsif degrees_of_freedom > 2
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degrees_of_freedom/(degrees_of_freedom - 2.0)
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end
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end
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# Quantile function extracted from http://www.jennessent.com/arcview/idf.htm
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# TODO: Make it truly Student's T sample.
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def random(elements: 1, seed: Random.new_seed)
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warn 'This is an alpha version code. The generated sample is similar to an uniform distribution'
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srand(seed)
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v = degrees_of_freedom
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results = []
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# Because the Quantile function of a student-t distribution is between (-Infinity, y)
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# we setup an small threshold in order to properly compute the integral
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threshold = 10_000.0e-12
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elements.times do
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y = rand
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results << Math.simpson_rule(threshold, y, 10_000) do |t|
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up = Math.gamma((v+1)/2.0)
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down = Math.sqrt(Math::PI * v) * Math.gamma(v/2.0)
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right = (1 + ((y ** 2)/v.to_f)) ** ((v+1)/2.0)
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left = up/down.to_f
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left * right
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end
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end
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if elements == 1
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results.first
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else
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results
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end
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end
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end
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end
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end
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