Module: BernoulliTrials

Includes:
Combinatorics, Math
Defined in:
lib/theory_of_probability.rb

Instance Method Summary collapse

Methods included from Combinatorics

#arrangement, #combination, #factorial

Instance Method Details

#bernoulli_formula_and_laplace_theorem(n, k, all, suc = -1)) ⇒ Object 



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# File 'lib/theory_of_probability.rb', line 220

def bernoulli_formula_and_laplace_theorem(n, k, all, suc = -1)
  if suc != -1
    p = suc.fdiv all
  else
    p = all
  end
  q = 1 - p
  if n * p * q < 9         # Laplace theorem give satisfactory approximation for n*p*q > 9, else Bernoulli formula
    combination(n, k) * (p ** k) * (q ** (n - k))          # Bernoulli formula C(n,k) * (p ^ k) * (q ^ (n-k))
  else
    gaussian_function((k - n * p).fdiv sqrt(n * p * q)).fdiv(sqrt(n * p * q))        # Laplace theorem φ((k - n*p)/sqrt(n*p*q)) / sqrt(n*p*q)
  end
end

#gaussian_function(x) ⇒ Object 



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# File 'lib/theory_of_probability.rb', line 234

def gaussian_function(x)
  if x < 0           # φ(-x) = φ(x)
    x * -1
  end
  exp(-(x ** 2) / 2).fdiv sqrt(2 * PI)      # φ(x) = exp(-(x^2/2)) / sqrt(2*π)
end