public void ConstructorTest()
{
#region doc_example1
// Create a new Generalized Pareto Distribution with mu = 0, sigma = 0.42, xi = 3
var pareto = new GeneralizedParetoDistribution(location: 0, scale: 0.42, shape: 3);
// Common measures
double mean = pareto.Mean; // -0.21
double median = pareto.Median; // 0.98
double var = pareto.Variance; // -0.00882
double mode = pareto.Mode; // 0.19185185523755152
// Cumulative distribution functions
double cdf = pareto.DistributionFunction(x: 1.4); // 0.55035568697739079
double ccdf = pareto.ComplementaryDistributionFunction(x: 1.4); // 0.44964431302260921
double icdf = pareto.InverseDistributionFunction(p: cdf); // 1.3999999035548829
// Probability density functions
double pdf = pareto.ProbabilityDensityFunction(x: 1.4); // 0.097325608879352654
double lpdf = pareto.LogProbabilityDensityFunction(x: 1.4); // -2.3296931293597707
// Hazard (failure rate) functions
double hf = pareto.HazardFunction(x: 1.4); // 0.21645021645021648
double chf = pareto.CumulativeHazardFunction(x: 1.4); // 0.79929842426612341
// String representation
string str = pareto.ToString(CultureInfo.InvariantCulture); // Pareto(x; μ = 0, σ = 0.42, ξ = 3)
#endregion
Assert.AreEqual(-0.21, mean);
Assert.AreEqual(0.98, median);
Assert.AreEqual(-0.008819999999999998, var);
Assert.AreEqual(0.19185185523755152, mode, 1e-10);
Assert.AreEqual(0.79929842426612341, chf);
Assert.AreEqual(0.55035568697739079, cdf);
Assert.AreEqual(0.097325608879352654, pdf);
Assert.AreEqual(-2.3296931293597707, lpdf);
Assert.AreEqual(0.21645021645021648, hf);
Assert.AreEqual(0.44964431302260921, ccdf);
Assert.AreEqual(1.40, icdf, 1e-5);
Assert.AreEqual("Pareto(x; μ = 0, σ = 0.42, ξ = 3)", str);
var range1 = pareto.GetRange(0.95);
var range2 = pareto.GetRange(0.99);
var range3 = pareto.GetRange(0.01);
Assert.AreEqual(0.023289267355975959, range1.Min, 1e-8);
Assert.AreEqual(1119.8599999998519, range1.Max, 1e-8);
Assert.AreEqual(0.0042854196206619614, range2.Min, 1e-8);
Assert.AreEqual(139999.86000000086, range2.Max, 1e-8);
Assert.AreEqual(0.0042854196206619493, range3.Min, 1e-8);
Assert.AreEqual(139999.86000000086, range3.Max, 1e-8);
}
public void ParetoDistributionConstructorTest()
{
double expected, actual;
{
var target = new GeneralizedParetoDistribution(0, 3.1, 4.42);
actual = target.ProbabilityDensityFunction(-1);
expected = 0.0;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(0);
expected = 0.32258064516129031;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(3.09);
expected = 0.040736023124121959;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(3.1);
expected = 0.040604655728907986;
Assert.AreEqual(expected, actual, 1e-7);
actual = target.ProbabilityDensityFunction(3.2);
expected = 0.039332127082599325;
Assert.AreEqual(expected, actual, 1e-7);
actual = target.ProbabilityDensityFunction(5.8);
expected = 0.021027167986227731;
Assert.AreEqual(expected, actual, 1e-7);
actual = target.ProbabilityDensityFunction(10);
expected = 0.011412447781534748;
Assert.AreEqual(expected, actual, 1e-7);
}
}
public void MedianTest()
{
var target = new GeneralizedParetoDistribution(0, scale: 7.12, shape: 2);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5), 1e-6);
}