function rational_approximation(t) {
// Abramowitz and Stegun formula 26.2.23.
// The absolute value of the error should be less than 4.5 e-4.
var c = [2.515517, 0.802853, 0.010328];
var d = [1.432788, 0.189269, 0.001308];
var numerator = (c[2]*t + c[1])*t + c[0];
var denominator = ((d[2]*t + d[1])*t + d[0])*t + 1.0;
return t - numerator / denominator;
}
function normal_cdf_inverse(p) {
// See article above for explanation of this section.
if (p < 0.5) {
// F^-1(p) = - G^-1(p)
return -rational_approximation( Math.sqrt(-2.0*Math.log(p)) );
} else {
// F^-1(p) = G^-1(1-p)
return rational_approximation( Math.sqrt(-2.0*Math.log(1.0-p)) );
}
}