public void cdf()
{
var e1 = new Dictionary <int, double>
{
{ 5, 0.081034388254077383 },
{ 10, 0.014498539552460298 },
{ 11, 0.0094071917739316415 },
{ 15, 0.0036762734018237525 }
};
var e2 = new Dictionary <int, double>
{
{ 5, 0.99999999278182994 },
{ 10, 1 },
{ 11, 1 },
{ 15, 1 }
};
foreach (int samples in new[] { 5, 10, 11, 15 })
{
var dist = new ShapiroWilkDistribution(samples: samples);
Assert.IsTrue(dist.Support.Min < dist.Support.Max);
double actual, e;
actual = dist.DistributionFunction(0);
Assert.AreEqual(0, actual, 1e-8);
actual = dist.DistributionFunction(1);
Assert.AreEqual(1, actual);
actual = dist.DistributionFunction(0.8);
e = e1[samples];
Assert.AreEqual(e, actual, 1e-10);
actual = dist.DistributionFunction(0.999999);
e = e2[samples];
Assert.AreEqual(e, actual, 1e-10);
actual = dist.DistributionFunction(-1);
Assert.AreEqual(0, actual);
actual = dist.DistributionFunction(2);
Assert.AreEqual(1, actual);
actual = dist.DistributionFunction(100);
Assert.AreEqual(1, actual);
actual = dist.DistributionFunction(double.PositiveInfinity);
Assert.AreEqual(1, actual);
actual = dist.DistributionFunction(double.NegativeInfinity);
Assert.AreEqual(0, actual);
}
}
public void ConstructorTest4()
{
// Create a new Shapiro-Wilk's W for 5 samples
var sw = new ShapiroWilkDistribution(samples: 5);
double mean = sw.Mean; // 0.8490362043845332
double median = sw.Median; // 0.8490362043845332
double mode = sw.Mode; // 0.8490362043845332
double cdf = sw.DistributionFunction(x: 0.84); // 0.16492187919271617
double pdf = sw.ProbabilityDensityFunction(x: 0.84); // 0.82021062372326459
double lpdf = sw.LogProbabilityDensityFunction(x: 0.84); // -0.1981941135071546
double ccdf = sw.ComplementaryDistributionFunction(x: 0.84); // 0.83507812080728383
double icdf = sw.InverseDistributionFunction(p: cdf); // 0.84000000194587177
double hf = sw.HazardFunction(x: 0.84); // 0.98219627994845971
double chf = sw.CumulativeHazardFunction(x: 0.84); // 0.18023000065451003
string str = sw.ToString(CultureInfo.InvariantCulture); // W(x; n = 12)
Assert.AreEqual(0.8490362043845332, mean);
Assert.AreEqual(0.8490362043845332, mode);
Assert.AreEqual(0.8490362043845332, median, 1e-8);
Assert.AreEqual(0.18023000065451003, chf);
Assert.AreEqual(0.16492187919271617, cdf);
Assert.AreEqual(0.82021062372326459, pdf);
Assert.AreEqual(-0.1981941135071546, lpdf);
Assert.AreEqual(0.98219627994845971, hf);
Assert.AreEqual(0.83507812080728383, ccdf);
Assert.AreEqual(0.84000000194587177, icdf, 1e-8);
Assert.AreEqual("W(x; n = 5)", str);
var range1 = sw.GetRange(0.95);
Assert.AreEqual(0.77509977845943778, range1.Min, 1e-6);
Assert.AreEqual(0.98299906816568339, range1.Max, 1e-6);
var range2 = sw.GetRange(0.99);
Assert.AreEqual(0.70180031139628618, range2.Min, 1e-6);
Assert.AreEqual(0.99334588234528642, range2.Max, 1e-6);
var range3 = sw.GetRange(0.01);
Assert.AreEqual(0.70180031139628618, range3.Min, 1e-6);
Assert.AreEqual(0.99334588234528642, range3.Max, 1e-6);
Assert.AreEqual(0, sw.Support.Min);
Assert.AreEqual(1, sw.Support.Max);
Assert.AreEqual(sw.InverseDistributionFunction(0), sw.Support.Min);
Assert.AreEqual(sw.InverseDistributionFunction(1), sw.Support.Max);
}
public void ConstructorTest3()
{
var sw = new ShapiroWilkDistribution(samples: 12);
double mean = sw.Mean; // 0.940148636841248
double median = sw.Median; // 0.940148636841248
double mode = sw.Mode; // 0.940148636841248
double cdf = sw.DistributionFunction(x: 0.42); // 4.8168255270011394E-06
double pdf = sw.ProbabilityDensityFunction(x: 0.42); // 0.000043477460596194137
double lpdf = sw.LogProbabilityDensityFunction(x: 0.42); // -10.043267901368219
double ccdf = sw.ComplementaryDistributionFunction(x: 0.42); // 0.999995183174473
double icdf = sw.InverseDistributionFunction(p: cdf); // 0.42000002275671627
double hf = sw.HazardFunction(x: 0.42); // 4.3477670020544943E-05
double chf = sw.CumulativeHazardFunction(x: 0.42); // 4.8168371279400235E-06
string str = sw.ToString(CultureInfo.InvariantCulture); // W(x; n = 12)
Assert.AreEqual(0.940148636841248, mean);
Assert.AreEqual(0.940148636841248, mode);
Assert.AreEqual(0.940148636841248, median, 1e-8);
Assert.AreEqual(4.8168371279400235E-06, chf);
Assert.AreEqual(4.8168255270011394E-06, cdf);
Assert.AreEqual(0.000043477460596194137, pdf);
Assert.AreEqual(-10.043267901368219, lpdf);
Assert.AreEqual(4.3477670020544943E-05, hf);
Assert.AreEqual(0.999995183174473, ccdf);
Assert.AreEqual(0.42000002275671627, icdf, 1e-8);
Assert.AreEqual("W(x; n = 12)", str);
var range1 = sw.GetRange(0.95);
Assert.AreEqual(0.8607805197002204, range1.Min, 1e-6);
Assert.AreEqual(0.97426955790462533, range1.Max, 1e-6);
var range2 = sw.GetRange(0.99);
Assert.AreEqual(0.80248479750351542, range2.Min, 1e-6);
Assert.AreEqual(0.98186388183806661, range2.Max, 1e-6);
var range3 = sw.GetRange(0.01);
Assert.AreEqual(0.80248479750351542, range3.Min, 1e-6);
Assert.AreEqual(0.98186388183806661, range3.Max, 1e-6);
Assert.AreEqual(0, sw.Support.Min);
Assert.AreEqual(1, sw.Support.Max);
Assert.AreEqual(sw.InverseDistributionFunction(0), sw.Support.Min);
Assert.AreEqual(sw.InverseDistributionFunction(1), sw.Support.Max);
}
public void inverse_cdf_simple()
{
var sw = new ShapiroWilkDistribution(samples: 12);
double cdf = sw.DistributionFunction(x: 0.42);
Assert.AreEqual(4.8168255270011394E-06, cdf);
double ccdf = sw.ComplementaryDistributionFunction(x: 0.42);
Assert.AreEqual(0.999995183174473, ccdf);
// Shapiro-Wilk support is inversed?
double icdf = sw.InverseDistributionFunction(p: cdf);
Assert.AreEqual(0.42000002275671627, icdf, 1e-8);
}
public void inverse_cdf()
{
foreach (int samples in new[] { 5, 10, 11, 15 })
{
var dist = new ShapiroWilkDistribution(samples: samples);
double[] percentiles = Vector.Range(0.49, 0.51, stepSize: 0.01);
for (int i = 0; i < percentiles.Length; i++)
{
double p = percentiles[i];
double icdf = dist.InverseDistributionFunction(p);
double cdf = dist.DistributionFunction(icdf);
Assert.AreEqual(p, cdf, 1e-5);
}
}
}
public void ConstructorTest2()
{
// Example from http://www.nag.com/numeric/cl/nagdoc_cl23/pdf/G01/g01ddc.pdf
double[] b =
{
1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, 1.11, 3.48,
1.10, 0.88, 0.51, 1.46, 0.52, 6.20, 1.69, 0.08, 3.67,
2.81, 3.49
};
var sw = new ShapiroWilkDistribution(b.Length);
double expected = 0.5246;
double actual = sw.DistributionFunction(0.9590);
Assert.AreEqual(expected, actual, 1e-3);
}
public void ConstructorTest()
{
// Example from http://www.nag.com/numeric/cl/nagdoc_cl23/pdf/G01/g01ddc.pdf
double[] a =
{
0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43,
0.21, 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97,
9.53, 4.55, 0.47, 6.66
};
var sw = new ShapiroWilkDistribution(a.Length);
double expected = 0.0421;
double actual = sw.DistributionFunction(0.9005);
Assert.AreEqual(expected, actual, 1e-4);
}