public void ConstructorTest()
{
double[] ranks = { 1, 2, 3, 4, 5 };
var mannWhitney = new MannWhitneyDistribution(ranks, n1: 2, n2: 3);
double mean = mannWhitney.Mean; // 2.7870954605658511
double median = mannWhitney.Median; // 1.5219615583481305
double var = mannWhitney.Variance; // 18.28163603621158
double cdf = mannWhitney.DistributionFunction(x: 4); // 0.6
double pdf = mannWhitney.ProbabilityDensityFunction(x: 4); // 0.2
double lpdf = mannWhitney.LogProbabilityDensityFunction(x: 4); // -1.6094379124341005
double ccdf = mannWhitney.ComplementaryDistributionFunction(x: 4); // 0.4
double icdf = mannWhitney.InverseDistributionFunction(p: cdf); // 3.6666666666666661
double hf = mannWhitney.HazardFunction(x: 4); // 0.5
double chf = mannWhitney.CumulativeHazardFunction(x: 4); // 0.916290731874155
string str = mannWhitney.ToString(); // MannWhitney(u; n1 = 2, n2 = 3)
Assert.AreEqual(3.0, mean);
Assert.AreEqual(3.0000006357828775, median);
Assert.AreEqual(3.0, var);
Assert.AreEqual(0.916290731874155, chf);
Assert.AreEqual(0.6, cdf);
Assert.AreEqual(0.2, pdf);
Assert.AreEqual(-1.6094379124341005, lpdf);
Assert.AreEqual(0.5, hf);
Assert.AreEqual(0.4, ccdf);
Assert.AreEqual(3.6666666666666661, icdf);
Assert.AreEqual("MannWhitney(u; n1 = 2, n2 = 3)", str);
}
public void ConstructorTest()
{
#region doc_create
double[] ranks = { 1, 2, 3, 4, 5 };
var mannWhitney = new MannWhitneyDistribution(ranks, n1: 2, n2: 3);
double mean = mannWhitney.Mean; // 2.7870954605658511
double median = mannWhitney.Median; // 1.5219615583481305
double var = mannWhitney.Variance; // 18.28163603621158
double mode = mannWhitney.Mode;
double cdf = mannWhitney.DistributionFunction(x: 4); // 0.6
double pdf = mannWhitney.ProbabilityDensityFunction(x: 4); // 0.2
double lpdf = mannWhitney.LogProbabilityDensityFunction(x: 4); // -1.6094379124341005
double ccdf = mannWhitney.ComplementaryDistributionFunction(x: 4); // 0.4
double icdf = mannWhitney.InverseDistributionFunction(p: cdf); // 3.6666666666666661
double hf = mannWhitney.HazardFunction(x: 4); // 0.5
double chf = mannWhitney.CumulativeHazardFunction(x: 4); // 0.916290731874155
string str = mannWhitney.ToString(); // MannWhitney(u; n1 = 2, n2 = 3)
#endregion
Assert.AreEqual(3.0, mean);
Assert.AreEqual(3.0, mode);
Assert.AreEqual(3.0000006357828775, median, 1e-5);
Assert.AreEqual(3.0, var, 1e-5);
Assert.AreEqual(0.916290731874155, chf, 1e-8);
Assert.AreEqual(0.8, cdf, 1e-8);
Assert.AreEqual(0.2, pdf, 1e-8);
Assert.AreEqual(-1.6094379124341005, lpdf, 1e-8);
Assert.AreEqual(0.5, hf, 1e-8);
Assert.AreEqual(0.4, ccdf, 1e-8);
Assert.AreEqual(4, icdf, 1e-8);
Assert.AreEqual("MannWhitney(u; n1 = 2, n2 = 3)", str);
var range1 = mannWhitney.GetRange(0.95);
var range2 = mannWhitney.GetRange(0.99);
var range3 = mannWhitney.GetRange(0.01);
Assert.AreEqual(0, range1.Min, 1e-5);
Assert.AreEqual(6, range1.Max, 1e-5);
Assert.AreEqual(-8.5830688476562492E-07, range2.Min, 1e-5);
Assert.AreEqual(6.0000005561746477, range2.Max, 1e-4);
Assert.AreEqual(-8.58306884765625E-07, range3.Min, 1e-5);
Assert.AreEqual(6.0000005561746477, range3.Max, 1e-5);
}
public void ApproximationTest()
{
int t = 14;
double[] m = Matrix.Magic(6).Reshape().Get(0, t * 2);
double[] samples = m.Rank();
double[] rank1 = samples.Get(0, t);
double[] rank2 = samples.Get(t, 0);
var exact = new MannWhitneyDistribution(rank1, rank2, exact: true);
var approx = new MannWhitneyDistribution(rank1, rank2, exact: false);
var nd = NormalDistribution.Estimate(exact.Table);
Assert.AreEqual(nd.Mean, exact.Mean, 1e-10);
Assert.AreEqual(nd.Variance, exact.Variance, 2e-5);
foreach (double x in Vector.Range(0, 100))
{
double e = approx.DistributionFunction(x);
double a = exact.DistributionFunction(x);
if (e > 0.23)
{
Assert.AreEqual(e, a, 0.1);
}
else
{
Assert.AreEqual(e, a, 0.01);
}
}
foreach (double x in Vector.Range(0, 100))
{
double e = approx.ComplementaryDistributionFunction(x);
double a = exact.ComplementaryDistributionFunction(x);
if (e > 0.23)
{
Assert.AreEqual(e, a, 0.1);
}
else
{
Assert.AreEqual(e, a, 0.01);
}
}
}
public void ConstructorTest()
{
double[] ranks = { 1, 2, 3, 4, 5 };
var mannWhitney = new MannWhitneyDistribution(ranks, n1: 2, n2: 3);
double mean = mannWhitney.Mean; // 2.7870954605658511
double median = mannWhitney.Median; // 1.5219615583481305
double var = mannWhitney.Variance; // 18.28163603621158
try { double mode = mannWhitney.Mode; Assert.Fail(); }
catch { }
double cdf = mannWhitney.DistributionFunction(x: 4); // 0.6
double pdf = mannWhitney.ProbabilityDensityFunction(x: 4); // 0.2
double lpdf = mannWhitney.LogProbabilityDensityFunction(x: 4); // -1.6094379124341005
double ccdf = mannWhitney.ComplementaryDistributionFunction(x: 4); // 0.4
double icdf = mannWhitney.InverseDistributionFunction(p: cdf); // 3.6666666666666661
double hf = mannWhitney.HazardFunction(x: 4); // 0.5
double chf = mannWhitney.CumulativeHazardFunction(x: 4); // 0.916290731874155
string str = mannWhitney.ToString(); // MannWhitney(u; n1 = 2, n2 = 3)
Assert.AreEqual(3.0, mean);
Assert.AreEqual(3.0000006357828775, median);
Assert.AreEqual(3.0, var);
Assert.AreEqual(0.916290731874155, chf);
Assert.AreEqual(0.6, cdf);
Assert.AreEqual(0.2, pdf);
Assert.AreEqual(-1.6094379124341005, lpdf);
Assert.AreEqual(0.5, hf);
Assert.AreEqual(0.4, ccdf);
Assert.AreEqual(3.6666666666666661, icdf);
Assert.AreEqual("MannWhitney(u; n1 = 2, n2 = 3)", str);
var range1 = mannWhitney.GetRange(0.95);
var range2 = mannWhitney.GetRange(0.99);
var range3 = mannWhitney.GetRange(0.01);
Assert.AreEqual(0.00000095367431640625085, range1.Min);
Assert.AreEqual(5.9999995430310555, range1.Max);
Assert.AreEqual(0, range2.Min);
Assert.AreEqual(6.000000194140088, range2.Max);
Assert.AreEqual(0, range3.Min);
Assert.AreEqual(6.000000194140088, range3.Max);
}
public void DistributionFunctionTest()
{
double[] ranks = { 1, 2, 3, 4, 5 };
int n1 = 2;
int n2 = 3;
int N = n1 + n2;
Assert.AreEqual(N, ranks.Length);
var target = new MannWhitneyDistribution(ranks, n1, n2);
// Number of possible combinations is 5!/(3!2!) = 10.
int nc = (int)Special.Binomial(5, 3);
Assert.AreEqual(10, nc);
double[] expected = { 0.1, 0.1, 0.2, 0.2, 0.2, 0.1, 0.1, 0.0, 0.0 };
expected = expected.CumulativeSum();
for (int i = 0; i < expected.Length; i++)
{
// P(U<=i)
double actual = target.DistributionFunction(i);
Assert.AreEqual(expected[i], actual, 1e-10);
}
expected = new double[] { 0.0, 0.0, 0.1, 0.1, 0.2, 0.2, 0.2, 0.1, 0.1 };
expected = expected.CumulativeSum().Reversed();
for (int i = 0; i < expected.Length; i++)
{
// P(U>i)
double actual = target.ComplementaryDistributionFunction(i);
Assert.AreEqual(expected[i], actual, 1e-10);
}
}