/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
public override double DistributionFunction(double x)
{
double z = (x - ksi) / omega;
double cdf = Accord.Math.Normal.Function(z) - 2 * OwensT.Function(z, alpha);
return(cdf);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
protected internal override double InnerDistributionFunction(double x)
{
double z = (x - ksi) / omega;
double cdf = Accord.Math.Normal.Function(z) - 2 * OwensT.Function(z, alpha);
return(cdf);
}
public void FunctionTest()
{
double[] a_vec =
{
0.2500000000000000E+00,
0.4375000000000000E+00,
0.9687500000000000E+00,
0.0625000000000000E+00,
0.5000000000000000E+00,
0.9999975000000000E+00,
0.5000000000000000E+00,
0.1000000000000000E+01,
0.2000000000000000E+01,
0.3000000000000000E+01,
0.5000000000000000E+00,
0.1000000000000000E+01,
0.2000000000000000E+01,
0.3000000000000000E+01,
0.5000000000000000E+00,
0.1000000000000000E+01,
0.2000000000000000E+01,
0.3000000000000000E+01,
0.5000000000000000E+00,
0.1000000000000000E+01,
0.2000000000000000E+01,
0.3000000000000000E+01,
0.5000000000000000E+00,
0.1000000000000000E+01,
0.2000000000000000E+01,
0.3000000000000000E+01,
0.1000000000000000E+02,
0.1000000000000000E+03
};
double[] h_vec =
{
0.0625000000000000E+00,
6.5000000000000000E+00,
7.0000000000000000E+00,
4.7812500000000000E+00,
2.0000000000000000E+00,
1.0000000000000000E+00,
0.1000000000000000E+01,
0.1000000000000000E+01,
0.1000000000000000E+01,
0.1000000000000000E+01,
0.5000000000000000E+00,
0.5000000000000000E+00,
0.5000000000000000E+00,
0.5000000000000000E+00,
0.2500000000000000E+00,
0.2500000000000000E+00,
0.2500000000000000E+00,
0.2500000000000000E+00,
0.1250000000000000E+00,
0.1250000000000000E+00,
0.1250000000000000E+00,
0.1250000000000000E+00,
0.7812500000000000E-02,
0.7812500000000000E-02,
0.7812500000000000E-02,
0.7812500000000000E-02,
0.7812500000000000E-02,
0.7812500000000000E-02
};
double[] t_vec =
{
3.8911930234701366E-02,
2.0005773048508315E-11,
6.3990627193898685E-13,
1.0632974804687463E-07,
8.6250779855215071E-03,
6.6741808978228592E-02,
0.4306469112078537E-01,
0.6674188216570097E-01,
0.7846818699308410E-01,
0.7929950474887259E-01,
0.6448860284750376E-01,
0.1066710629614485E+00,
0.1415806036539784E+00,
0.1510840430760184E+00,
0.7134663382271778E-01,
0.1201285306350883E+00,
0.1666128410939293E+00,
0.1847501847929859E+00,
0.7317273327500385E-01,
0.1237630544953746E+00,
0.1737438887583106E+00,
0.1951190307092811E+00,
0.7378938035365546E-01,
0.1249951430754052E+00,
0.1761984774738108E+00,
0.1987772386442824E+00,
0.2340886964802671E+00,
0.2479460829231492E+00
};
double[,] table =
{
// H A T T
// (Tabulated) (TFN) DIFF
{ 0.0625, 0.2500, 0.0389119302347014, 0.0389119302347014, 0 },
{ 6.5000, 0.4375, 0.0000000000200058, 0.0000000000100105, 9.995e-12 },
{ 7.0000, 0.9688, 0.0000000000006399, 0.0000000000003200, 3.2e-13 },
{ 4.7812, 0.0625, 0.0000001063297480, 0.0000001063297480, 2.647e-23 },
{ 2.0000, 0.5000, 0.0086250779855215, 0.0086250779855215, 1.735e-18 },
{ 1.0000, 1.0000, 0.0667418089782286, 0.0667418089782286, 0 },
{ 1.0000, 0.5000, 0.0430646911207854, 0.0430646911207854, 0 },
{ 1.0000, 1.0000, 0.0667418821657010, 0.0667418821657010, 0 },
{ 1.0000, 2.0000, 0.0784681869930841, 0.0784681869930841, 0 },
{ 1.0000, 3.0000, 0.0792995047488726, 0.0792995047488726, 1.388e-17 },
{ 0.5000, 0.5000, 0.0644886028475038, 0.0644886028475038, 1.388e-17 },
{ 0.5000, 1.0000, 0.1066710629614485, 0.1066710629614485, 1.388e-17 },
{ 0.5000, 2.0000, 0.1415806036539784, 0.1415806036539784, 0 },
{ 0.5000, 3.0000, 0.1510840430760184, 0.1510840430760184, 2.776e-17 },
{ 0.2500, 0.5000, 0.0713466338227178, 0.0713466338227178, 2.776e-17 },
{ 0.2500, 1.0000, 0.1201285306350883, 0.1201285306350883, 0 },
{ 0.2500, 2.0000, 0.1666128410939293, 0.1666128410939293, 2.776e-17 },
{ 0.2500, 3.0000, 0.1847501847929859, 0.1847501847929859, 2.776e-17 },
{ 0.1250, 0.5000, 0.0731727332750039, 0.0731727332750039, 0 },
{ 0.1250, 1.0000, 0.1237630544953746, 0.1237630544953746, 2.776e-17 },
{ 0.1250, 2.0000, 0.1737438887583106, 0.1737438887583106, 0 },
{ 0.1250, 3.0000, 0.1951190307092811, 0.1951190307092811, 2.776e-17 },
{ 0.0078, 0.5000, 0.0737893803536555, 0.0737893803536555, 1.388e-17 },
{ 0.0078, 1.0000, 0.1249951430754052, 0.1249951430754052, 0 },
{ 0.0078, 2.0000, 0.1761984774738108, 0.1761984774738108, 2.776e-17 },
{ 0.0078, 3.0000, 0.1987772386442824, 0.1987772386442823, 5.551e-17 },
{ 0.0078, 10.0000, 0.2340886964802671, 0.2340886964802671, 2.776e-17 },
{ 0.0078, 100.0000, 0.2479460829231492, 0.2479460829231492, 0 },
};
for (int i = 0; i < table.GetLength(0); i++)
{
double H = h_vec[i];
double A = a_vec[i];
double tabulated = t_vec[i];
double expected = table[i, 3];
double actual = OwensT.Function(H, A);
Assert.AreEqual(expected, actual, 1e-10);
}
}
public void ExampleTest()
{
double x = OwensT.Function(h: 2, a: 42);
Assert.AreEqual(0.011375065974089608, x);
}
