public void ConstructorTest()
{
// Create a new Anderson Darling distribution (A²) for comparing against a Gaussian
var a2 = new AndersonDarlingDistribution(AndersonDarlingDistributionType.Normal, 30);
double median = a2.Median; // 0.33089957635450062
double chf = a2.CumulativeHazardFunction(x: 0.27); // 0.42618068373640966
double cdf = a2.DistributionFunction(x: 0.27); // 0.34700165471995292
double ccdf = a2.ComplementaryDistributionFunction(x: 0.27); // 0.65299834528004708
double icdf = a2.InverseDistributionFunction(p: cdf); // 0.27000000012207787
string str = a2.ToString(CultureInfo.InvariantCulture); // "A²(x; n = 30)"
Assert.AreEqual(0.33089957635450062, median);
Assert.AreEqual(0.42618068373640966, chf);
Assert.AreEqual(0.34700165471995292, cdf);
Assert.AreEqual(0.65299834528004708, ccdf);
Assert.AreEqual(0.27, icdf, 1e-6);
Assert.AreEqual("A²(x; n = 30)", str);
Assert.IsFalse(Double.IsNaN(median));
var range1 = a2.GetRange(0.95);
var range2 = a2.GetRange(0.99);
var range3 = a2.GetRange(0.01);
Assert.AreEqual(0.1552371857564955, range1.Min);
Assert.AreEqual(0.73303544269106991, range1.Max);
Assert.AreEqual(0.11507415861447158, range2.Min);
Assert.AreEqual(1.0, range2.Max);
Assert.AreEqual(0.1150741586144715, range3.Min);
Assert.AreEqual(1.0, range3.Max);
}
public void inverse_cdf_uniform()
{
var a2 = new AndersonDarlingDistribution(AndersonDarlingDistributionType.Uniform, 30);
Assert.AreEqual(0, a2.InverseDistributionFunction(0));
Assert.AreEqual(Double.PositiveInfinity, a2.InverseDistributionFunction(1));
Assert.AreEqual(6.0001199778679908d, a2.InverseDistributionFunction(0.999));
Assert.AreEqual(0, a2.DistributionFunction(0));
Assert.AreEqual(0.64343026173645557d, a2.DistributionFunction(1));
Assert.AreEqual(0.90775461488067177d, a2.DistributionFunction(2));
double[] percentiles = Vector.Range(0.0, 1.0, stepSize: 0.1);
{
double p = 0.5;
double icdf = a2.InverseDistributionFunction(p);
double cdf = a2.DistributionFunction(icdf);
Assert.AreEqual(cdf, 0.5, 0.05);
}
for (int i = 0; i < percentiles.Length; i++)
{
if (i == 5)
{
continue;
}
double p = percentiles[i];
double icdf = a2.InverseDistributionFunction(p);
double cdf = a2.DistributionFunction(icdf);
Assert.AreEqual(cdf, p, 1e-5);
}
}
public void inverse_cdf()
{
var a2 = new AndersonDarlingDistribution(AndersonDarlingDistributionType.Normal, 30);
Assert.AreEqual(0, a2.InverseDistributionFunction(0));
Assert.AreEqual(Double.PositiveInfinity, a2.InverseDistributionFunction(1));
Assert.AreEqual(1.4047406720947551d, a2.InverseDistributionFunction(0.999));
Assert.AreEqual(1.4615690610009224E-06d, a2.DistributionFunction(0));
Assert.AreEqual(0.98946087159962637d, a2.DistributionFunction(1));
Assert.AreEqual(0.99996831752075233d, a2.DistributionFunction(2));
double[] percentiles = Vector.Range(0.0, 1.0, stepSize: 0.1);
{
double p = 0.5;
double icdf = a2.InverseDistributionFunction(p);
double cdf = a2.DistributionFunction(icdf);
Assert.AreEqual(cdf, 0.5, 0.05);
}
for (int i = 0; i < percentiles.Length; i++)
{
if (i == 5)
{
continue;
}
double p = percentiles[i];
double icdf = a2.InverseDistributionFunction(p);
double cdf = a2.DistributionFunction(icdf);
Assert.AreEqual(cdf, p, 1e-5);
}
}
public void uniform_test()
{
// Create a new Anderson Darling distribution (A²) for comparing against a Uniform distribution
var a2 = new AndersonDarlingDistribution(AndersonDarlingDistributionType.Uniform, 10);
double median = a2.Median;
double chf = a2.CumulativeHazardFunction(x: 0.27);
double cdf = a2.DistributionFunction(x: 0.27);
double ccdf = a2.ComplementaryDistributionFunction(x: 0.27);
double icdf = a2.InverseDistributionFunction(p: cdf);
string str = a2.ToString(CultureInfo.InvariantCulture); // "A²(x; n = 30)"
Assert.AreEqual(0.76936270639003257, median, 1e-6);
Assert.AreEqual(0.0424239540571123, chf, 1e-6);
Assert.AreEqual(0.041536650001198654, cdf, 1e-6);
Assert.AreEqual(0.95846334999880134, ccdf, 1e-6);
Assert.AreEqual(0.27, icdf, 1e-6);
Assert.AreEqual("A²(x; n = 10)", str);
Assert.IsFalse(Double.IsNaN(median));
var range1 = a2.GetRange(0.95);
var range2 = a2.GetRange(0.99);
var range3 = a2.GetRange(0.01);
Assert.AreEqual(0.28254198132705227, range1.Min, 1e-6);
Assert.AreEqual(2.5127111321231137, range1.Max, 1e-6);
Assert.AreEqual(0.20232764997988909, range2.Min, 1e-6);
Assert.AreEqual(3.9195747018635374, range2.Max, 1e-6);
Assert.AreEqual(0.20232764997988903, range3.Min, 1e-6);
Assert.AreEqual(3.9195747018635374, range3.Max, 1e-6);
Assert.AreEqual(0, a2.Support.Min);
Assert.AreEqual(Double.PositiveInfinity, a2.Support.Max);
Assert.AreEqual(a2.InverseDistributionFunction(0), a2.Support.Min);
Assert.AreEqual(a2.InverseDistributionFunction(1), a2.Support.Max);
}
