public void MeanTest()
{
NoncentralTDistribution target;
target = new NoncentralTDistribution(3, 5);
Assert.AreEqual(6.90988298942671, target.Mean);
Assert.AreEqual(30.2535170724314, target.Variance);
target = new NoncentralTDistribution(1.1, 5);
Assert.AreEqual(44.672931414521223, target.Mean);
Assert.IsTrue(Double.IsNaN(target.Variance));
target = new NoncentralTDistribution(4.2, -2);
Assert.AreEqual(-2.4746187622053673, target.Mean);
Assert.AreEqual(3.42171652719572, target.Variance);
target = new NoncentralTDistribution(0.047, 55);
Assert.IsTrue(Double.IsNaN(target.Mean));
Assert.IsTrue(Double.IsNaN(target.Variance));
target = new NoncentralTDistribution(2.1, -0.42);
Assert.AreEqual(-0.71446479359810855, target.Mean);
Assert.AreEqual(24.19394005870879, target.Variance);
target = new NoncentralTDistribution(5.97, -42);
Assert.AreEqual(-48.390832208385575, target.Mean);
Assert.AreEqual(312.49612392294557, target.Variance);
}
public void ConstructorTest2()
{
var distribution = new NoncentralTDistribution(
degreesOfFreedom: 4, noncentrality: 2.42);
double mean = distribution.Mean; // 3.0330202123035104
double median = distribution.Median; // 2.6034842414893795
double var = distribution.Variance; // 4.5135883917583683
double cdf = distribution.DistributionFunction(x: 1.4); // 0.15955740661144721
double pdf = distribution.ProbabilityDensityFunction(x: 1.4); // 0.23552141805184526
double lpdf = distribution.LogProbabilityDensityFunction(x: 1.4); // -1.4459534225195116
double ccdf = distribution.ComplementaryDistributionFunction(x: 1.4); // 0.84044259338855276
double icdf = distribution.InverseDistributionFunction(p: cdf); // 1.4000000000123853
double hf = distribution.HazardFunction(x: 1.4); // 0.28023498559521387
double chf = distribution.CumulativeHazardFunction(x: 1.4); // 0.17382662901507062
string str = distribution.ToString(CultureInfo.InvariantCulture); // T(x; df = 4, μ = 2.42)
Assert.AreEqual(3.0330202123035104, mean);
Assert.AreEqual(2.6034842414893795, median);
Assert.AreEqual(4.5135883917583683, var);
Assert.AreEqual(0.17382662901507062, chf);
Assert.AreEqual(0.15955740661144721, cdf);
Assert.AreEqual(0.23552141805184526, pdf);
Assert.AreEqual(-1.4459534225195116, lpdf);
Assert.AreEqual(0.28023498559521387, hf);
Assert.AreEqual(0.84044259338855276, ccdf);
Assert.AreEqual(1.4000000000123853, icdf);
Assert.AreEqual("T(x; df = 4, μ = 2.42)", str);
}
public void DistributionFunctionTest()
{
double[,] table =
{
// x d df expected
{ 3.00, 0.0, 1, 0.8975836176504333 },
{ 3.00, 0.0, 2, 0.9522670169 },
{ 3.00, 0.0, 3, 0.9711655571887813 },
{ 3.00, 0.5, 1, 0.8231218863999999 },
{ 3.00, 0.5, 2, 0.904902151 },
{ 3.00, 0.5, 3, 0.9363471834 },
{ 3.00, 1.0, 1, 0.7301025986 },
{ 3.00, 1.0, 2, 0.8335594263 },
{ 3.00, 1.0, 3, 0.8774010255 },
{ 3.00, 2.0, 1, 0.5248571617 },
{ 3.00, 2.0, 2, 0.6293856597 },
{ 3.00, 2.0, 3, 0.6800271741 },
{ 3.00, 4.0, 1, 0.20590131975 },
{ 3.00, 4.0, 2, 0.2112148916 },
{ 3.00, 4.0, 3, 0.2074730718 },
{ 15.00, 7.0, 15, 0.9981130072 },
{ 15.00, 7.0, 20, 0.999487385 },
{ 15.00, 7.0, 25, 0.9998391562 },
{ 0.05, 1.0, 1, 0.168610566972 },
{ 0.05, 1.0, 2, 0.16967950985 },
{ 0.05, 1.0, 3, 0.1701041003 },
{ 4.00, 2.0, 10, 0.9247683363 },
{ 4.00, 3.0, 10, 0.7483139269 },
{ 4.00, 4.0, 10, 0.4659802096 },
{ 5.00, 2.0, 10, 0.9761872541 },
{ 5.00, 3.0, 10, 0.8979689357 },
{ 5.00, 4.0, 10, 0.7181904627 },
{ 6.00, 2.0, 10, 0.9923658945 },
{ 6.00, 3.0, 10, 0.9610341649 },
{ 6.00, 4.0, 10, 0.868800735 },
};
for (int i = 0; i < table.GetLength(0); i++)
{
double x = table[i, 0];
double delta = table[i, 1];
double df = table[i, 2];
var target = new NoncentralTDistribution(df, delta);
double expected = table[i, 3];
double actual = target.DistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-10);
}
}
public void ConstructorTest2()
{
var distribution = new NoncentralTDistribution(
degreesOfFreedom: 4, noncentrality: 2.42);
double mean = distribution.Mean; // 3.0330202123035104
double median = distribution.Median; // 2.6034842414893795
double var = distribution.Variance; // 4.5135883917583683
double mode = distribution.Mode; // 2.0940683409246641
double cdf = distribution.DistributionFunction(x: 1.4); // 0.15955740661144721
double pdf = distribution.ProbabilityDensityFunction(x: 1.4); // 0.23552141805184526
double lpdf = distribution.LogProbabilityDensityFunction(x: 1.4); // -1.4459534225195116
double ccdf = distribution.ComplementaryDistributionFunction(x: 1.4); // 0.84044259338855276
double icdf = distribution.InverseDistributionFunction(p: cdf); // 1.4000000000123853
double hf = distribution.HazardFunction(x: 1.4); // 0.28023498559521387
double chf = distribution.CumulativeHazardFunction(x: 1.4); // 0.17382662901507062
string str = distribution.ToString(CultureInfo.InvariantCulture); // T(x; df = 4, μ = 2.42)
Assert.AreEqual(3.0330202123035104, mean);
Assert.AreEqual(2.6034842414893795, median);
Assert.AreEqual(4.5135883917583683, var);
Assert.AreEqual(2.0940683409246641, mode);
Assert.AreEqual(0.17382662901507062, chf);
Assert.AreEqual(0.15955740661144721, cdf);
Assert.AreEqual(0.23552141805184526, pdf);
Assert.AreEqual(-1.4459534225195116, lpdf);
Assert.AreEqual(0.28023498559521387, hf);
Assert.AreEqual(0.84044259338855276, ccdf);
Assert.AreEqual(1.4000000000123853, icdf);
Assert.AreEqual("T(x; df = 4, μ = 2.42)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(0.7641009341279591, range1.Min);
Assert.AreEqual(6.6668131011180742, range1.Max);
Assert.AreEqual(0.098229727233034247, range2.Min);
Assert.AreEqual(10.541194525031729, range2.Max);
Assert.AreEqual(0.09822972723303551, range3.Min);
Assert.AreEqual(10.541194525031729, range3.Max);
}
/// <summary>
/// Computes the power for a test with givens values of
/// <see cref="IPowerAnalysis.Effect">effect size</see> and <see cref="IPowerAnalysis.Samples">
/// number of samples</see> under <see cref="IPowerAnalysis.Size"/>.
/// </summary>
///
/// <returns>
/// The power for the test under the given conditions.
/// </returns>
///
public override void ComputePower()
{
double delta = Effect / Math.Sqrt(1.0 / Samples1 + 1.0 / Samples2);
double df = Samples1 + Samples2 - 2;
TDistribution td = new TDistribution(df);
NoncentralTDistribution nt = new NoncentralTDistribution(df, delta);
switch (Tail)
{
case DistributionTail.TwoTail:
{
double Ta = td.InverseDistributionFunction(1.0 - Size / 2);
double pa = nt.ComplementaryDistributionFunction(+Ta);
double pb = nt.DistributionFunction(-Ta);
Power = pa + pb;
break;
}
case DistributionTail.OneLower:
{
double Ta = td.InverseDistributionFunction(Size);
Power = nt.DistributionFunction(Ta);
break;
}
case DistributionTail.OneUpper:
{
double Ta = td.InverseDistributionFunction(1.0 - Size);
Power = nt.ComplementaryDistributionFunction(Ta);
break;
}
default:
throw new InvalidOperationException();
}
}
public void ProbabilityFunctionTest()
{
double[,] table =
{
// x d df expected
{ 3.00, 0.0, 1, 0.03183098861 },
{ 3.00, 0.0, 2, 0.02741012223 },
{ 3.00, 0.0, 3, 0.02297203730 },
{ 3.00, 0.5, 1, 0.05359565579 },
{ 3.00, 0.5, 2, 0.05226515196 },
{ 3.00, 0.5, 3, 0.04788249161 },
{ 3.00, 7.0, 15, 0.0009236578208725 },
{ 15.00, 7.0, 15, 0.0013850587855 },
{ 15.00, 7.0, 25, 0.00018206084230 },
{ 0.00, 7.0, 25, 0.0000000000090438 },
{ 0.00, 2.0, 1, 0.0430785586036 },
{ 0.00, 2.0, 2, 0.047848248255205 },
{ 0.00, 2.0, 3, 0.0497428348122 },
{ 0.00, 4.0, 1, 0.000106781070 },
{ 0.00, 4.0, 2, 0.000118603949 },
};
for (int i = 0; i < table.GetLength(0); i++)
{
double x = table[i, 0];
double delta = table[i, 1];
double df = table[i, 2];
var target = new NoncentralTDistribution(df, delta);
double expected = table[i, 3];
double actual = target.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-10);
}
}
public void MedianTest()
{
NoncentralTDistribution target = new NoncentralTDistribution(3.2, 4.57);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
