/// <summary>
/// Mean of a truncated normal distribution
/// </summary>
/// <param name="mean">mean of underlying normal distribution</param>
/// <param name="sd">standard devition of underlying normal distribution</param>
/// <param name="a">support lower bound</param>
/// <param name="b">support upper bound</param>
/// <returns></returns>
public static double Mean(double mean, double sd, double a, double b)
{
var aNorm = (a - mean) / sd;
var bNorm = (b - mean) / sd;
var z = StandardNormalDistribution.Cdf(bNorm) - StandardNormalDistribution.Cdf(aNorm);
return(mean + (StandardNormalDistribution.Pdf(aNorm) - StandardNormalDistribution.Pdf(bNorm)) / z * sd);
}
/// <summary>
/// Probability density function of a truncated normal distribution
/// </summary>
/// <param name="x">parameter</param>
/// <param name="mean">mean of underlying normal distribution</param>
/// <param name="sd">standard deviation of underlying normal distribution</param>
/// <param name="a">support lower bound</param>
/// <param name="b">support upper bound</param>
/// <returns>PDF of a truncated normal distribution</returns>
public static double Pdf(double x, double mean, double sd, double a, double b)
{
var xNorm = (x - mean) / sd;
var aNorm = (a - mean) / sd;
var bNorm = (b - mean) / sd;
var z = StandardNormalDistribution.Cdf(bNorm) - StandardNormalDistribution.Cdf(aNorm);
return(StandardNormalDistribution.Pdf(xNorm) / (sd * z));
}