Module: Quantiles

Defined in:
lib/quantiles.rb

Class Method Summary collapse

Class Method Details

.cauchy(p) ⇒ Object 



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# File 'lib/quantiles.rb', line 51

def cauchy(p)
  (0..1).include? p or raise "#{p}: outside probability domain [0,1]"
  Math.tan(Math::PI*(0.5-p))
end

.normal(p) ⇒ Object

approximation from Peter J. Acklam



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# File 'lib/quantiles.rb', line 4

def normal(p)
  (Float::EPSILON..1-Float::EPSILON).include? p or
    raise "#{p}: outside probabiliy domain (0,1)"
  a = [ -3.969683028665376e+01,  2.209460984245205e+02,
        -2.759285104469687e+02,  1.383577518672690e+02,
        -3.066479806614716e+01,  2.506628277459239e+00 ]
  b = [ -5.447609879822406e+01,  1.615858368580409e+02,
        -1.556989798598866e+02,  6.680131188771972e+01,
        -1.328068155288572e+01 ]
  c = [ -7.784894002430293e-03, -3.223964580411365e-01,
        -2.400758277161838e+00, -2.549732539343734e+00,
         4.374664141464968e+00,  2.938163982698783e+00 ]
  d = [  7.784695709041462e-03,  3.224671290700398e-01,
         2.445134137142996e+00,  3.754408661907416e+00 ]
  if p < 0.02425 then # lower region
    q = Math.sqrt(-2*Math.log(p))
    (((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) /
     ((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1)
  elsif p < 0.97575 then # central region (symmetrical)
    q = p - 0.5
    r = q*q
    (((((a[0]*r+a[1])*r+a[2])*r+a[3])*r+a[4])*r+a[5])*q /
    (((((b[0]*r+b[1])*r+b[2])*r+b[3])*r+b[4])*r+1)
  else # upper region
    q = Math.sqrt(-2*Math.log(1-p))
    -(((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) /
      ((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1)
  end
end

.triangular(p) ⇒ Object 



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# File 'lib/quantiles.rb', line 41

def triangular(p)
  (0..1).include? p or raise "#{p}: outside probability domain [0,1]"
  if p < 0.5
    -0.5 + Math.sqrt( 0.5*p )
  else # symmetric reflection
     0.5 - Math.sqrt( 0.5*(1-p) )
  end
end

.uniform(p) ⇒ Object 



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# File 'lib/quantiles.rb', line 35

def uniform(p)
  (0..1).include? p or raise "#{p}: outside probability domain [0,1]"
  p-0.5
end