/// <summary>
/// This function return the cummulative distribution function (CDF)
/// for Fisher Distribution with X from 0 to x and number degree of freedoms
/// are k1 and k2.
/// </summary>
/// <param name="x">double. x</param>
/// <param name="k1">int. k1 is firt number degree of freedom</param>
/// <param name="k2">int. k2 is second number degree of freedom</param>
/// <returns>
/// The value of cummulative distribution function (CDF)
/// for Fisher Distribution with X from 0 to x and number degree of freedoms
/// are k1 and k2.
/// </returns>
public static double CDF(double x, int k1, int k2)
{
// number degree of freedoms and x must greater than 0
if (!(k1 > 0 && k2 > 0 && x > 0))
{
return(double.NaN);
}
FisherFunction function = new FisherFunction(k1, k2);
return(Integrator.GaussLegendre(function, 0, x, 1.0e-6));
}
/// <summary>
/// This function return the cummulative distribution function (CDF)
/// for ChiSquare Distribution where X2 from 0 t x2 and
/// number degree of freedom k.
/// </summary>
/// <param name="x2">double. x2</param>
/// <param name="k">int. k is number degree of freedom</param>
/// <returns>
/// The value of cummulative distribution function (CDF)
/// for ChiSquare Distribution where X2 form 0 t x2 and
/// number degree of freedom k.
/// </returns>
public static double CDF(double x2, int k)
{
// the number degree of freedom must be
// more or equal than 1. The value of x must be
// not less than 0
if (k < 1 || x2 < 0)
{
return(double.NaN);
}
ChiSquareFunction function = new ChiSquareFunction(k);
return(Integrator.GaussLegendre(function, 0, x2, 1.0e-6));
}
/// <summary>
/// This function return the cummulative distribution function (CDF)
/// for Student's t distribution less than t and number degree of
/// freedom k.
/// </summary>
/// <param name="t">double. t</param>
/// <param name="k">int. k is number degree of freedom</param>
/// <returns>
/// The value of cummulative distribution function (CDF)
/// for Student's t distribution less than t and number degree of
/// freedom k.
/// </returns>
public static double CDF(double t, int k)
{
// number degree of freedom must be mor than 0
if (k <= 0)
{
return(double.NaN);
}
if (t == 0)
{
return(0.5);
}
StudentFunction function = new StudentFunction(k);
if (t < 0)
{
return(0.5 - Integrator.GaussLegendre(function, t, 0, 1.0e-6));
}
else
{
return(0.5 + Integrator.GaussLegendre(function, 0, t, 1.0e-6));
}
}
/// <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));
}
}