/// <summary>
///Cumulative normal distribution function
///For this implementation see M. Abramowitz and I. Stegun,
///Handbook of Mathematical Functions,
///Dover Publications, New York (1972)
/// </summary>
public static double Cumulative(double z)
{
if (z <= Cdf_Asymptotic_First_Threshold)
{
// Asymptotic expansion for very negative z following (26.2.12) on page 408
// in M. Abramowitz and A. Stegun, Pocketbook of Mathematical Functions, ISBN 3-87144818-4.
double sum = 1;
if (z >= CdfAsymptoticSecondThreshold)
{
double zsqr = z * z, i = 1, g = 1, a = double.MaxValue, lasta;
do
{
lasta = a;
double x = (4 * i - 3) / zsqr;
double y = x * ((4 * i - 1) / zsqr);
a = g * (x - y);
sum -= a;
g *= y;
++i;
a = Math.Abs(a);
} while (lasta > a && a >= Math.Abs(sum * DoubleUtils.MachineEpsilon));
}
return(-Density(z) * sum / z);
}
return(0.5 * ErrorFunctions.Erfc(-z * MathConsts.InvSqrt2));
}
private static double NormalizedCall(double d)
{
return(Math.Exp(-0.5 * d * d) * (MathConsts.InvSqrtTwoPi - 0.5 * d * ErrorFunctions.Erfcx(MathConsts.InvSqrt2 * d)));
}
