class Statistics::Distribution::TStudent
Attributes
degrees_of_freedom[RW]
mode[R]
Public Class Methods
new(v)
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# File lib/statistics/distribution/t_student.rb, line 7 def initialize(v) self.degrees_of_freedom = v @mode = 0 end
Public Instance Methods
cumulative_function(value)
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Extracted from codeplea.com/incomplete-beta-function-c This function is shared under zlib license and the author is Lewis Van Winkle
# File lib/statistics/distribution/t_student.rb, line 14 def cumulative_function(value) upper = (value + Math.sqrt(value * value + degrees_of_freedom)) lower = (2.0 * Math.sqrt(value * value + degrees_of_freedom)) x = upper/lower alpha = degrees_of_freedom/2.0 beta = degrees_of_freedom/2.0 Math.incomplete_beta_function(x, alpha, beta) end
density_function(value)
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# File lib/statistics/distribution/t_student.rb, line 26 def density_function(value) return if degrees_of_freedom <= 0 upper = Math.gamma((degrees_of_freedom + 1)/2.0) lower = Math.sqrt(degrees_of_freedom * Math::PI) * Math.gamma(degrees_of_freedom/2.0) left = upper/lower right = (1 + ((value ** 2)/degrees_of_freedom.to_r)) ** -((degrees_of_freedom + 1)/2.0) left * right end
mean()
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# File lib/statistics/distribution/t_student.rb, line 37 def mean 0 if degrees_of_freedom > 1 end
random(elements: 1, seed: Random.new_seed)
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Quantile function extracted from www.jennessent.com/arcview/idf.htm TODO: Make it truly Student's T sample.
# File lib/statistics/distribution/t_student.rb, line 51 def random(elements: 1, seed: Random.new_seed) warn 'This is an alpha version code. The generated sample is similar to an uniform distribution' srand(seed) v = degrees_of_freedom results = [] # Because the Quantile function of a student-t distribution is between (-Infinity, y) # we setup an small threshold in order to properly compute the integral threshold = 10_000.0e-12 elements.times do y = rand results << Math.simpson_rule(threshold, y, 10_000) do |t| up = Math.gamma((v+1)/2.0) down = Math.sqrt(Math::PI * v) * Math.gamma(v/2.0) right = (1 + ((y ** 2)/v.to_r)) ** ((v+1)/2.0) left = up/down.to_r left * right end end if elements == 1 results.first else results end end
variance()
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# File lib/statistics/distribution/t_student.rb, line 41 def variance if degrees_of_freedom > 1 && degrees_of_freedom <= 2 Float::INFINITY elsif degrees_of_freedom > 2 degrees_of_freedom/(degrees_of_freedom - 2.0) end end