Class: RubyStatistics::Distribution::F

Inherits:
Object
  • Object
show all
Defined in:
lib/ruby-statistics/distribution/f.rb

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(k, j) ⇒ F

Returns a new instance of F.



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# File 'lib/ruby-statistics/distribution/f.rb', line 6

def initialize(k, j)
  self.d1 = k
  self.d2 = j
end

Instance Attribute Details

#d1 ⇒ Object

Degrees of freedom #1 and #2



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# File 'lib/ruby-statistics/distribution/f.rb', line 4

def d1
  @d1
end

#d2 ⇒ Object

Degrees of freedom #1 and #2



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# File 'lib/ruby-statistics/distribution/f.rb', line 4

def d2
  @d2
end

Instance Method Details

#cumulative_function(value) ⇒ Object

Formula extracted from www.itl.nist.gov/div898/handbook/eda/section3/eda3665.htm#CDF



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# File 'lib/ruby-statistics/distribution/f.rb', line 12

def cumulative_function(value)
  k = d2/(d2 + d1 * value.to_r)

  1 - Math.incomplete_beta_function(k, d2/2.0, d1/2.0)
end

#density_function(value) ⇒ Object 



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# File 'lib/ruby-statistics/distribution/f.rb', line 18

def density_function(value)
  return if d1 < 0 || d2 < 0 # F-pdf is well defined for the [0, +infinity) interval.

  val = value.to_r
  upper = ((d1 * val) ** d1) * (d2**d2)
  lower = (d1 * val + d2) ** (d1 + d2)
  up = Math.sqrt(upper/lower.to_r)
  down = val * Math.beta_function(d1/2.0, d2/2.0)

  up/down.to_r
end

#mean ⇒ Object 



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# File 'lib/ruby-statistics/distribution/f.rb', line 30

def mean
  return if d2 <= 2

  d2/(d2 - 2).to_r
end

#mode ⇒ Object 



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# File 'lib/ruby-statistics/distribution/f.rb', line 36

def mode
  return if d1 <= 2

  left = (d1 - 2)/d1.to_r
  right = d2/(d2 + 2).to_r

  (left * right).to_f
end