public void ConstructorTest()
{
var F = new FDistribution(degrees1: 8, degrees2: 5);
double mean = F.Mean; // 1.6666666666666667
double median = F.Median; // 1.0545096252132447
double var = F.Variance; // 7.6388888888888893
double cdf = F.DistributionFunction(x: 0.27); // 0.049463408057268315
double pdf = F.ProbabilityDensityFunction(x: 0.27); // 0.45120469723580559
double lpdf = F.LogProbabilityDensityFunction(x: 0.27); // -0.79583416831212883
double ccdf = F.ComplementaryDistributionFunction(x: 0.27); // 0.95053659194273166
double icdf = F.InverseDistributionFunction(p: cdf); // 0.27
double hf = F.HazardFunction(x: 0.27); // 0.47468419528555084
double chf = F.CumulativeHazardFunction(x: 0.27); // 0.050728620222091653
string str = F.ToString(CultureInfo.InvariantCulture); // F(x; df1 = 8, df2 = 5)
Assert.AreEqual(1.6666666666666667, mean);
Assert.AreEqual(1.0545096252132447, median);
Assert.AreEqual(7.6388888888888893, var);
Assert.AreEqual(0.050728620222091653, chf);
Assert.AreEqual(0.049463408057268315, cdf);
Assert.AreEqual(0.45120469723580559, pdf);
Assert.AreEqual(-0.79583416831212883, lpdf);
Assert.AreEqual(0.47468419528555084, hf);
Assert.AreEqual(0.95053659194273166, ccdf);
Assert.AreEqual(0.27, icdf);
Assert.AreEqual("F(x; df1 = 8, df2 = 5)", str);
}
/// <summary>
/// Creates a new F-Test for a given statistic
/// with given degrees of freedom.
/// </summary>
///
/// <param name="statistic">The test statistic.</param>
/// <param name="d1">The degrees of freedom for the numerator.</param>
/// <param name="d2">The degrees of freedom for the denominator.</param>
///
public FTest(double statistic, int d1, int d2)
: base(statistic)
{
base.Hypothesis = Hypothesis.OneUpper;
StatisticDistribution = new FDistribution(d1, d2);
PValue = 1.0 - StatisticDistribution.DistributionFunction(statistic);
}
public void ConstructorTest()
{
var F = new FDistribution(degrees1: 8, degrees2: 5);
double mean = F.Mean; // 1.6666666666666667
double median = F.Median; // 1.0545096252132447
double var = F.Variance; // 7.6388888888888893
double mode = F.Mode; // 0.5357142857142857
double cdf = F.DistributionFunction(x: 0.27); // 0.049463408057268315
double pdf = F.ProbabilityDensityFunction(x: 0.27); // 0.45120469723580559
double lpdf = F.LogProbabilityDensityFunction(x: 0.27); // -0.79583416831212883
double ccdf = F.ComplementaryDistributionFunction(x: 0.27); // 0.95053659194273166
double icdf = F.InverseDistributionFunction(p: cdf); // 0.27
double hf = F.HazardFunction(x: 0.27); // 0.47468419528555084
double chf = F.CumulativeHazardFunction(x: 0.27); // 0.050728620222091653
string str = F.ToString(CultureInfo.InvariantCulture); // F(x; df1 = 8, df2 = 5)
Assert.AreEqual(1.6666666666666667, mean);
Assert.AreEqual(1.0545096252132447, median);
Assert.AreEqual(7.6388888888888893, var);
Assert.AreEqual(0.5357142857142857, mode);
Assert.AreEqual(0.050728620222091653, chf);
Assert.AreEqual(0.049463408057268315, cdf);
Assert.AreEqual(0.45120469723580559, pdf);
Assert.AreEqual(-0.79583416831212883, lpdf);
Assert.AreEqual(0.47468419528555084, hf);
Assert.AreEqual(0.95053659194273166, ccdf);
Assert.AreEqual(0.27, icdf);
Assert.AreEqual("F(x; df1 = 8, df2 = 5)", str);
var range1 = F.GetRange(0.95);
var range2 = F.GetRange(0.99);
var range3 = F.GetRange(0.01);
Assert.AreEqual(0.27118653875813753, range1.Min);
Assert.AreEqual(4.8183195356568689, range1.Max);
Assert.AreEqual(0.15078805233761733, range2.Min);
Assert.AreEqual(10.289311046135927, range2.Max);
Assert.AreEqual(0.1507880523376173, range3.Min);
Assert.AreEqual(10.289311046135927, range3.Max);
}
public void Confirm_BetPrimeDistribution_Relative_to_F_Distribution()
{
double alpha = 4.0d;
double beta = 6.0d;
FDistribution fdist = new FDistribution((int)alpha * 2, (int)beta * 2);
double fMean = fdist.Mean;
double fPdf = (beta / alpha) * fdist.ProbabilityDensityFunction(4.0d);
double fCdf = fdist.DistributionFunction(4.0d);
var betaPrimeDist = new BetaPrimeDistribution(alpha, beta);
double bpMean = (beta / alpha) * betaPrimeDist.Mean;
double bpPdf = betaPrimeDist.ProbabilityDensityFunction((alpha / beta) * 4.0d);
double bpCdf = betaPrimeDist.DistributionFunction((alpha / beta) * 4.0d);
Assert.AreEqual(fMean, bpMean, 0.00000001, "mean should be equal");
Assert.AreEqual(fPdf, bpPdf, 0.00000001, "probability density should be equal");
Assert.AreEqual(fCdf, bpCdf, 0.00000001, "cumulative distribution should be equal");
//Beta Prime distribution is a scaled version of Pearson Type VI, which itself is scale of F distribution
}
public void MeanVarianceTest()
{
int[] d = { 1, 2, 3, 4, 5 };
double[] mean = { double.NaN, double.NaN, 3.0000, 2.0000, 1.6667 };
double[] var = { double.NaN, double.NaN, double.NaN, double.NaN, 8.8889 };
for (int i = 0; i < 5; i++)
{
FDistribution f = new FDistribution(d[i], d[i]);
if (double.IsNaN(mean[i]))
Assert.IsTrue(double.IsNaN(f.Mean));
else Assert.AreEqual(mean[i], f.Mean, 1e-4);
if (double.IsNaN(var[i]))
Assert.IsTrue(double.IsNaN(f.Variance));
else Assert.AreEqual(var[i], f.Variance, 1e-4);
}
}
public void InverseDistributionFunctionTest()
{
double[] cdf =
{
0.231238, 0.404508, 0.605516, 0.86038, 1.20711, 1.71825, 2.5611, 4.23607, 9.24342
};
FDistribution target = new FDistribution(4, 2);
for (int i = 0; i < cdf.Length; i++)
{
double x = (i + 1) / 10.0;
double actual = target.InverseDistributionFunction(x);
double expected = cdf[i];
Assert.AreEqual(expected, actual, 1e-5);
Assert.IsFalse(double.IsNaN(actual));
}
}
public void LogProbabilityDistributionFunctionTest2()
{
FDistribution f = new FDistribution(2, 2);
double actual;
double expected;
double x;
for (int i = 1; i <= 6; i++)
{
x = i;
actual = f.LogProbabilityDensityFunction(x);
expected = System.Math.Log(f.ProbabilityDensityFunction(x));
Assert.AreEqual(expected, actual, 1e-10);
}
for (int i = 5; i <= 10; i++)
{
f = new FDistribution(i, i);
x = 3;
actual = f.LogProbabilityDensityFunction(x);
expected = System.Math.Log(f.ProbabilityDensityFunction(x));
Assert.AreEqual(expected, actual, 1e-10);
}
}
public void ProbabilityDistributionFunctionTest2()
{
FDistribution f = new FDistribution(2, 2);
Assert.AreEqual(f.ProbabilityDensityFunction(1), 0.2500, 1e-4);
Assert.AreEqual(f.ProbabilityDensityFunction(2), 0.1111, 1e-4);
Assert.AreEqual(f.ProbabilityDensityFunction(3), 0.0625, 1e-4);
Assert.AreEqual(f.ProbabilityDensityFunction(4), 0.0400, 1e-4);
Assert.AreEqual(f.ProbabilityDensityFunction(5), 0.0278, 1e-4);
Assert.AreEqual(f.ProbabilityDensityFunction(6), 0.0204, 1e-4);
Assert.AreEqual(new FDistribution(5, 5).ProbabilityDensityFunction(3), 0.0689, 1e-4);
Assert.AreEqual(new FDistribution(6, 6).ProbabilityDensityFunction(3), 0.0659, 1e-4);
Assert.AreEqual(new FDistribution(7, 7).ProbabilityDensityFunction(3), 0.0620, 1e-4);
Assert.AreEqual(new FDistribution(8, 8).ProbabilityDensityFunction(3), 0.0577, 1e-4);
Assert.AreEqual(new FDistribution(9, 9).ProbabilityDensityFunction(3), 0.0532, 1e-4);
Assert.AreEqual(new FDistribution(10, 10).ProbabilityDensityFunction(3), 0.0487, 1e-4);
}
public void LogProbabilityDistributionFunctionTest()
{
FDistribution f = new FDistribution(2, 3);
double expected = System.Math.Log(0.487139289628747);
double actual = f.LogProbabilityDensityFunction(0.5);
Assert.AreEqual(expected, actual, 1e-6);
}
public void DistributionFunctionTest3()
{
double[] cdf =
{
0, 0.0277778, 0.0816327, 0.140625, 0.197531, 0.25,
0.297521, 0.340278, 0.378698, 0.413265, 0.444444
};
FDistribution target = new FDistribution(4, 2);
for (int i = 0; i < 11; i++)
{
double x = i / 10.0;
double actual = target.DistributionFunction(x);
double expected = cdf[i];
Assert.AreEqual(expected, actual, 1e-5);
Assert.IsFalse(double.IsNaN(actual));
}
}
public void ComplementaryDistributionFunctionTest()
{
double actual;
double expected;
int[] nu1 = { 1, 2, 3, 4, 5 };
int[] nu2 = { 6, 7, 8, 9, 10 };
double[] x = { 2, 3, 4, 5, 6 };
double[] cdf = { 0.7930, 0.8854, 0.9481, 0.9788, 0.9919 };
FDistribution f;
for (int i = 0; i < 5; i++)
{
f = new FDistribution(nu1[i], nu2[i]);
expected = cdf[i];
actual = f.DistributionFunction(x[i]);
Assert.AreEqual(expected, actual, 1e-4);
f = new FDistribution(nu2[i], nu1[i]);
actual = f.ComplementaryDistributionFunction(1.0 / x[i]);
Assert.AreEqual(expected, actual, 1e-4);
}
}
public void MedianTest()
{
FDistribution target = new FDistribution(2, 3);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void DistributionFunctionTest()
{
FDistribution f = new FDistribution(2, 3);
Assert.AreEqual(f.DegreesOfFreedom1, 2);
Assert.AreEqual(f.DegreesOfFreedom2, 3);
double expected = 0.350480947161671;
double actual = f.DistributionFunction(0.5);
Assert.AreEqual(expected, actual, 1e-6);
}