public void Constructor_ExtensiveTestForDocumentation()
{
// Create a new Beta-Prime distribution with shape (4,2)
var betaPrime = new BetaPrimeDistribution(alpha: 4, beta: 2);
double mean = betaPrime.Mean; // 4.0
double median = betaPrime.Median; // 2.1866398762435981
double mode = betaPrime.Mode; // 1.0
double var = betaPrime.Variance; // +inf
double cdf = betaPrime.DistributionFunction(x: 0.4); // 0.02570357589099781
double pdf = betaPrime.ProbabilityDensityFunction(x: 0.4); // 0.16999719504628183
double lpdf = betaPrime.LogProbabilityDensityFunction(x: 0.4); // -1.7719733417957513
double ccdf = betaPrime.ComplementaryDistributionFunction(x: 0.4); // 0.97429642410900219
double icdf = betaPrime.InverseDistributionFunction(p: cdf); // 0.39999982363709291
double hf = betaPrime.HazardFunction(x: 0.4); // 0.17448200654307533
double chf = betaPrime.CumulativeHazardFunction(x: 0.4); // 0.026039684773113869
string str = betaPrime.ToString(CultureInfo.InvariantCulture); // BetaPrime(x; α = 4, β = 2)
Assert.AreEqual(4, betaPrime.Alpha);
Assert.AreEqual(2, betaPrime.Beta);
Assert.AreEqual(4.0, mean);
Assert.AreEqual(2.1866398762435981, median);
Assert.AreEqual(1.0, mode);
Assert.AreEqual(double.PositiveInfinity, var);
Assert.AreEqual(0.026039684773113869, chf);
Assert.AreEqual(0.02570357589099781, cdf);
Assert.AreEqual(0.16999719504628183, pdf);
Assert.AreEqual(-1.7719733417957513, lpdf);
Assert.AreEqual(0.17448200654307533, hf);
Assert.AreEqual(0.97429642410900219, ccdf);
Assert.AreEqual(0.39999982363709291, icdf);
Assert.AreEqual("BetaPrime(x; α = 4, β = 2)", str);
var range1 = betaPrime.GetRange(0.95);
var range2 = betaPrime.GetRange(0.99);
var range3 = betaPrime.GetRange(0.01);
Assert.AreEqual(0.52112465307247502, range1.Min);
Assert.AreEqual(12.082089043372052, range1.Max);
Assert.AreEqual(0.28546647531958014, range2.Min);
Assert.AreEqual(29.597777621141635, range2.Max);
Assert.AreEqual(range2.Min, range3.Min, 1e-15);
Assert.AreEqual(range2.Max, range3.Max, 1e-15);
}
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
}