/// <summary>
/// Shortfall.
/// </summary>
/// <param name="target"></param>
/// <param name="mean"></param>
/// <param name="std"></param>
/// <returns></returns>
public static double Shortfall(double target, double mean, double std)
{
var gIntegral =
new CumulativeNormalDistribution(mean, std);
return(gIntegral.Value(target));
}
/// <summary>
/// Average shortfall.
/// </summary>
/// <param name="target"></param>
/// <param name="mean"></param>
/// <param name="std"></param>
/// <returns></returns>
public static double AverageShortfall(double target, double mean, double std)
{
var gIntegral =
new CumulativeNormalDistribution(mean, std);
var g = new NormalDistribution(mean, std);
return((target - mean) * gIntegral.Value(target) +
std * std * g.Value(target));
}