Class: Statistics::Distribution::Normal

Inherits:
Object
  • Object
show all
Defined in:
lib/statistics/distribution/normal.rb

Direct Known Subclasses

StandardNormal

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(avg, std) ⇒ Normal

Returns a new instance of Normal.



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# File 'lib/statistics/distribution/normal.rb', line 7

def initialize(avg, std)
  self.mean = avg.to_f
  self.standard_deviation = std.to_f
  self.variance = std.to_f**2
end

Instance Attribute Details

#mean ⇒ Object Also known as: mode

Returns the value of attribute mean.



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# File 'lib/statistics/distribution/normal.rb', line 4

def mean
  @mean
end

#standard_deviation ⇒ Object

Returns the value of attribute standard_deviation.



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# File 'lib/statistics/distribution/normal.rb', line 4

def standard_deviation
  @standard_deviation
end

#variance ⇒ Object

Returns the value of attribute variance.



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# File 'lib/statistics/distribution/normal.rb', line 4

def variance
  @variance
end

Instance Method Details

#cumulative_function(value) ⇒ Object 



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# File 'lib/statistics/distribution/normal.rb', line 13

def cumulative_function(value)
  (1/2.0) * (1.0 + Math.erf((value - mean)/(standard_deviation * Math.sqrt(2.0))))
end

#density_function(value) ⇒ Object 



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# File 'lib/statistics/distribution/normal.rb', line 17

def density_function(value)
  return 0 if standard_deviation <= 0

  up_right = (value - mean)**2.0
  down_right = 2.0 * variance
  right = Math.exp(-(up_right/down_right))
  left_down = Math.sqrt(2.0 * Math::PI * variance)
  left_up = 1.0

  (left_up/(left_down) * right)
end

#random(elements: 1, seed: Random.new_seed) ⇒ Object

Marsaglia polar method implementation for random gaussian (normal) number generation. References: en.wikipedia.org/wiki/Marsaglia_polar_method math.stackexchange.com/questions/69245/transform-uniform-distribution-to-normal-distribution-using-lindeberg-l%C3%A9vy-clt www.projectrhea.org/rhea/index.php/The_principles_for_how_to_generate_random_samples_from_a_Gaussian_distribution



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# File 'lib/statistics/distribution/normal.rb', line 35

def random(elements: 1, seed: Random.new_seed)
  results = []

  # Setup seed
  srand(seed)

  # Number of random numbers to be generated.
  elements.times do
    x, y, r = 0.0, 0.0, 0.0

    # Find an (x, y) point in the x^2 + y^2 < 1 circumference.
    loop do
      x = 2.0 * rand - 1.0
      y = 2.0 * rand - 1.0

      r = (x ** 2) + (y ** 2)

      break unless r >= 1.0 || r == 0
    end

    # Project the random point to the required random distance
    r = Math.sqrt(-2.0 * Math.log(r) / r)

    # Transform the random distance to a gaussian value and append it to the results array
    results << mean + x * r * standard_deviation
  end

  if elements == 1
    results.first
  else
    results
  end
end