inverse_cdf.jl

function invnorm(p)
#Coefficients in rational approximations.
a = zeros(6);
a[1] = -3.969683028665376e+01
a[2] =  2.209460984245205e+02
a[3] = -2.759285104469687e+02
a[4] = 1.383577518672690e+02
a[5] = -3.066479806614716e+01
a[6] =  2.506628277459239e+00

b = zeros(5);
b[1] = -5.447609879822406e+01
b[2] =  1.615858368580409e+02
b[3] = -1.556989798598866e+02
b[4] =  6.680131188771972e+01
b[5] = -1.328068155288572e+01

c = zeros(6);
c[1] = -7.784894002430293e-03
c[2] = -3.223964580411365e-01
c[3] = -2.400758277161838e+00
c[4] = -2.549732539343734e+00
c[5] =  4.374664141464968e+00
c[6] =  2.938163982698783e+00

d = zeros(4);
d[1] =  7.784695709041462e-03
d[2] =   3.224671290700398e-01
d[3] =   2.445134137142996e+00
d[4] =   3.754408661907416e+00

#Define break-points.
p_low  = 0.02425;
p_high = 1 - p_low;

   #Rational approximation for lower region.
   if ((0 < p) && (p < p_low))
      q = sqrt(-2*log(p))
      x = (((((c[1]*q+c[2])*q+c[3])*q+c[4])*q+c[5])*q+c[6]) /
            ((((d[1]*q+d[2])*q+d[3])*q+d[4])*q+1)
   end

   #Rational approximation for central region.
   if ((p_low <= p) && (p <= p_high))
      q = p - 0.5
      r = q*q
      x = (((((a[1]*r+a[2])*r+a[3])*r+a[4])*r+a[5])*r+a[6])*q /
           (((((b[1]*r+b[2])*r+b[3])*r+b[4])*r+b[5])*r+1)
   end

   #Rational approximation for upper region.
   if ((p_high < p) && (p < 1))
      q = sqrt(-2*log(1-p))
      x = -(((((c[1]*q+c[2])*q+c[3])*q+c[4])*q+c[5])*q+c[6]) /
             ((((d[1]*q+d[2])*q+d[3])*q+d[4])*q+1)
   end

   if p == 0
      x = -Inf;
   elseif p == 1
      x = Inf;
   end

   return x;
end