| public ProbabilityDensityFunction ( double x ) : double | ||
| x | double | A single point in the distribution range. |
| return | double | |
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);
}
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 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 ProbabilityDistributionFunctionTest()
{
FDistribution f = new FDistribution(2, 3);
double expected = 0.487139289628747;
double actual = f.ProbabilityDensityFunction(0.5);
Assert.AreEqual(expected, actual, 1e-6);
}