///
/// Normal density function - Gaussian function
///
///
///
///
///
static double NormalDensityFunction(double x, double mean, double stdDev)
{
double Z = (x - mean);
Z = Z * Z;
Z = -(Z / (2 * stdDev * stdDev));
double normDist = (1 / Math.Sqrt(2 * Math.PI * stdDev)) * (Math.Exp(Z));
return normDist;
// Or
// return Math.Exp(-(Math.Pow((x - mean) / stdDev, 2) / 2)) / Math.Sqrt(2 * Math.PI) / stdDev;
}
///
/// Standard normal density function - mean = 0 and stdDev=1
///
///
///
static double NormalDensityFunctionStd(double Zscore)
{
double Z = -(Zscore * Zscore) / 2;
double normDist = (1 / Math.Sqrt(2 * Math.PI)) * (Math.Exp(Z));
return normDist;
}
///
/// Cumulative density function of a standard normal (Gaussian) random variable
/// Area under the normal density function from -inf to x
///
///
///
static double NormalCDF(double x)
{
const double a1 = 0.254829592;
const double a2 = -0.284496736;
const double a3 = 1.421413741;
const double a4 = -1.453152027;
const double a5 = 1.061405429;
const double p = 0.3275911;
// Save the sign of x
double sign = 1;
if (x < 0)
{
sign = -1;
x = x * -1;
}
x = x / Math.Sqrt(2.0);
//A&S formula 7.1.26
double t = 1.0 / (1.0 + p * x);
double y = 1.0 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * Math.Exp(-x * x);
return 0.5 * (1.0 + sign * y);
}
