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);
}
/// <summary>
/// Creates a new object that is a copy of the current instance.
/// </summary>
/// <returns>
/// A new object that is a copy of this instance.
/// </returns>
///
public override object Clone()
{
var clone = new MannWhitneyDistribution(NumberOfSamples1, NumberOfSamples2);
clone.exact = exact;
clone.table = table;
clone.n1 = n1;
clone.n2 = n2;
clone.Correction = Correction;
clone.approximation = (NormalDistribution)approximation.Clone();
return(clone);
}
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);
}
private void init(int n1, int n2, double[] ranks, bool?exact)
{
int n = n1 + n2;
this.n1 = n1;
this.n2 = n2;
// From https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test: For large samples, U
// is approximately normally distributed. In that case, the standardized value is given
// by z = (U - mean) / stdDev where:
double mean = (n1 * n2) / 2.0;
double stdDev = Math.Sqrt((n1 * n2 * (n + 1)) / 12.0);
bool hasVectors = ranks != null;
// For small samples (< 30) the distribution can be exact
this.exact = hasVectors && (n1 <= 30 && n2 <= 30);
if (exact.HasValue)
{
if (exact.Value && !hasVectors)
{
throw new ArgumentException("exact", "Cannot use exact method if rank vectors are not specified.");
}
this.exact = exact.Value; // force
}
if (hasVectors)
{
// Apply correction to the variance
double correction = MannWhitneyDistribution.correction(ranks);
stdDev = Math.Sqrt((n1 * n2 * ((n + 1.0) - correction)) / 12.0);
if (this.exact)
{
initExactMethod(ranks);
}
}
this.approximation = new NormalDistribution(mean, stdDev);
}
private void init(int n1, int n2, double[] ranks, bool?exact)
{
if (n1 <= 0)
{
throw new ArgumentOutOfRangeException("n1", "The number of observations in the first sample (n1) must be higher than zero.");
}
if (n2 <= 0)
{
throw new ArgumentOutOfRangeException("n2", "The number of observations in the second sample (n2) must be higher than zero.");
}
if (n1 > n2)
{
Trace.TraceWarning("Creating a MannWhitneyDistribution where the first sample is larger than the second sample. If possible, please re-organize your samples such that the first sample is smaller than the second sample.");
}
if (ranks != null)
{
if (ranks.Length <= 1)
{
throw new ArgumentOutOfRangeException("ranks", "The rank vector must contain a minimum of 2 elements.");
}
for (int i = 0; i < ranks.Length; i++)
{
if (ranks[i] < 0)
{
throw new ArgumentOutOfRangeException("The rank values cannot be negative.");
}
}
}
int n = n1 + n2;
this.n1 = n1;
this.n2 = n2;
// From https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test: For large samples, U
// is approximately normally distributed. In that case, the standardized value is given
// by z = (U - mean) / stdDev where:
double mean = ((double)n1 * n2) / 2.0;
double stdDev = Math.Sqrt(((double)n1 * n2 * (n + 1)) / 12.0);
bool hasVectors = ranks != null;
// For small samples (< 30) the distribution can be exact
this.exact = hasVectors && (n1 <= 30 && n2 <= 30);
if (exact.HasValue)
{
if (exact.Value && !hasVectors)
{
throw new ArgumentException("exact", "Cannot use exact method if rank vectors are not specified.");
}
this.exact = exact.Value; // force
}
if (hasVectors)
{
// Apply correction to the variance
double correction = MannWhitneyDistribution.correction(ranks);
double a = ((double)n1 * n2) / 12.0;
double b = (n + 1.0) - correction;
stdDev = Math.Sqrt(a * b);
if (this.exact)
{
initExactMethod(ranks);
}
}
this.approximation = new NormalDistribution(mean, stdDev);
}
public void ProbabilityDensityFunctionTest()
{
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 };
double sum = 0;
for (int i = 0; i < expected.Length; i++)
{
// P(U=i)
double actual = target.ProbabilityDensityFunction(i);
Assert.AreEqual(expected[i], actual);
sum += actual;
}
Assert.AreEqual(1, sum);
}
public void MedianTest()
{
double[] ranks = { 1, 1, 2, 3, 4, 7, 5 };
int n1 = 4;
int n2 = 3;
Assert.AreEqual(n1 + n2, ranks.Length);
var target = new MannWhitneyDistribution(ranks, n1, n2);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
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 = { 0.0, 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);
}
}
