public void ConstructorTest()
{
var pareto = new ParetoDistribution(scale: 0.42, shape: 3);
double mean = pareto.Mean; // 0.63
double median = pareto.Median; // 0.52916684095584676
double var = pareto.Variance; // 0.13229999999999997
double cdf = pareto.DistributionFunction(x: 1.4); // 0.973
double pdf = pareto.ProbabilityDensityFunction(x: 1.4); // 0.057857142857142857
double lpdf = pareto.LogProbabilityDensityFunction(x: 1.4); // -2.8497783609309111
double ccdf = pareto.ComplementaryDistributionFunction(x: 1.4); // 0.027000000000000024
double icdf = pareto.InverseDistributionFunction(p: cdf); // 1.4000000446580794
double hf = pareto.HazardFunction(x: 1.4); // 2.142857142857141
double chf = pareto.CumulativeHazardFunction(x: 1.4); // 3.6119184129778072
string str = pareto.ToString(CultureInfo.InvariantCulture); // Pareto(x; xm = 0.42, α = 3)
Assert.AreEqual(0.63, mean);
Assert.AreEqual(0.52916684095584676, median);
Assert.AreEqual(0.13229999999999997, var);
Assert.AreEqual(3.6119184129778072, chf);
Assert.AreEqual(0.973, cdf);
Assert.AreEqual(0.057857142857142857, pdf);
Assert.AreEqual(-2.8497783609309111, lpdf);
Assert.AreEqual(2.142857142857141, hf);
Assert.AreEqual(0.027000000000000024, ccdf);
Assert.AreEqual(1.40, icdf, 1e-7);
Assert.AreEqual("Pareto(x; xm = 0.42, α = 3)", str);
}
public void ConstructorTest()
{
var pareto = new ParetoDistribution(scale: 0.42, shape: 3);
double mean = pareto.Mean; // 0.63
double median = pareto.Median; // 0.52916684095584676
double var = pareto.Variance; // 0.13229999999999997
double mode = pareto.Mode; // 0.42
double cdf = pareto.DistributionFunction(x: 1.4); // 0.973
double pdf = pareto.ProbabilityDensityFunction(x: 1.4); // 0.057857142857142857
double lpdf = pareto.LogProbabilityDensityFunction(x: 1.4); // -2.8497783609309111
double ccdf = pareto.ComplementaryDistributionFunction(x: 1.4); // 0.027000000000000024
double icdf = pareto.InverseDistributionFunction(p: cdf); // 1.4000000446580794
double hf = pareto.HazardFunction(x: 1.4); // 2.142857142857141
double chf = pareto.CumulativeHazardFunction(x: 1.4); // 3.6119184129778072
string str = pareto.ToString(CultureInfo.InvariantCulture); // Pareto(x; xm = 0.42, α = 3)
Assert.AreEqual(0.63, mean);
Assert.AreEqual(0.52916684095584676, median);
Assert.AreEqual(0.13229999999999997, var);
Assert.AreEqual(0.42, mode, 1e-10);
Assert.AreEqual(3.6119184129778072, chf);
Assert.AreEqual(0.973, cdf);
Assert.AreEqual(0.057857142857142857, pdf);
Assert.AreEqual(-2.8497783609309111, lpdf);
Assert.AreEqual(2.142857142857141, hf);
Assert.AreEqual(0.027000000000000024, ccdf);
Assert.AreEqual(1.40, icdf, 1e-7);
Assert.AreEqual("Pareto(x; xm = 0.42, α = 3)", str);
var range1 = pareto.GetRange(0.95);
var range2 = pareto.GetRange(0.99);
var range3 = pareto.GetRange(0.01);
Assert.AreEqual(0.42724297039643383, range1.Min, 1e-8);
Assert.AreEqual(1.1400554029735852, range1.Max, 1e-8);
Assert.AreEqual(0.42140940651872005, range2.Min, 1e-8);
Assert.AreEqual(1.9494675279346789, range2.Max, 1e-8);
Assert.AreEqual(0.42140940651872005, range3.Min, 1e-8);
Assert.AreEqual(1.9494675279346789, range3.Max, 1e-8);
}
public void ParetoDistributionConstructorTest()
{
double expected, actual;
{
ParetoDistribution target = new ParetoDistribution(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 = 0.0;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(3.09);
expected = 0.0;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(3.1);
expected = 1.4258064;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(3.2);
expected = 1.20040576;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(5.8);
expected = 0.0478037;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(10);
expected = 0.00249598;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void FitWeights()
{
var source = new ParetoDistribution(scale: 7.12, shape: 2);
var sample = new double[10000];
var step = 1.0 / sample.Length;
for (var i = 0; i < sample.Length; i++)
sample[i] = source.InverseDistributionFunction(i * step);
var target = new ParetoDistribution();
double[] weights = Matrix.Vector(sample.Length, 1.0 / sample.Length);
target.Fit(sample, weights);
Assert.AreEqual(7.12, target.Scale, 1e-6);
Assert.AreEqual(2.0, target.Alpha, 1e-2);
}
public void MedianTest()
{
var target = new ParetoDistribution(scale: 7.12, shape: 2);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5), 1e-6);
}
public void FitTest()
{
var source = new ParetoDistribution(scale: 7.12, shape: 2);
var sample = new double[10000];
var step = 1.0 / sample.Length;
for (var i = 0; i < sample.Length; i++)
sample[i] = source.InverseDistributionFunction(i * step);
var target = new ParetoDistribution(0, 0);
target.Fit(sample);
Assert.AreEqual(7.12, target.Scale, 1e-6);
Assert.AreEqual(2.0, target.Alpha, 1e-2);
}
