/// <summary>
/// This function return the value of probability density
/// function(PDF) for normal standard distribution with Z=z
/// and Z ~ N(0,1)
/// </summary>
/// <param name="z">double. z is standard value</param>
/// <returns>
/// The value of probability density function (PDF) for x
/// where Z ~ N(0, 1)
/// </returns>
public static double PDF(double z)
{
NormalFunction function = new NormalFunction();
return function.Value(z);
}
/// <summary>
/// Return the cumulative distribution function (CDF)
/// for normal standard distribution with mean 0, standard
/// deviation 1 and Z has a value less than z
/// </summary>
/// <param name="z">
/// double. z is standard value where Z ~ N(0, 1)
/// </param>
/// <returns>
/// The cumulative distribution function for normal
/// standard distribution has a value less then z
/// </returns>
public static double CDF(double z)
{
// The CDF value for z < -10 --> 0
if (z < -10.0) return double.Epsilon;
// The CDF value for z > 10 --> 1
if (z > 10.0) return (1.0 - double.Epsilon);
NormalFunction function = new NormalFunction(0.0, 1.0);
// accuracy of the integration method is 1.0e-6
if (z < 0) return 0.5 - Integrator.GaussLegendre(function, z, 0, 1.0e-6);
else return 0.5 + Integrator.GaussLegendre(function, 0, z, 1.0e-6);
}
/// <summary>
/// This function return the value of probability density
/// function(PDF) for normal distribution with X=x, mean mu,
/// and standard deviation sig.
/// </summary>
/// <param name="x">double. x is observing data</param>
/// <param name="mu">double. mu is mean of data</param>
/// <param name="sig">double. sig is standard deviation data</param>
/// <returns>
/// The value of probability density function (PDF) for x
/// where X ~ N(mu, sig)
/// </returns>
public static double PDF(double x, double mu, double sig)
{
NormalFunction function = new NormalFunction(mu, sig);
return function.Value(x);
}
