public void EquivalencyTest1()
{
// when mu = sigma / ksi, the shifted log-logistic reduces to the log-logistic distribution.
double sigma = 4.2; // scale
double ksi = 0.42; // shape
double mu = sigma / ksi; // location
var target = new ShiftedLogLogisticDistribution(location: mu, scale: sigma, shape: ksi);
var log = LogLogisticDistribution.FromLocationShape(location: mu, shape: ksi);
Assert.AreEqual(log.Mean, target.Mean, 1e-10);
Assert.AreEqual(log.Median, target.Median);
Assert.AreEqual(log.Mode, target.Mode, 1e-10);
Assert.AreEqual(log.Variance, target.Variance, 1e-10);
double actual, expected;
for (double i = -10; i < 10; i += 0.1)
{
expected = log.DistributionFunction(i);
actual = target.DistributionFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-5));
expected = log.ProbabilityDensityFunction(i);
actual = target.ProbabilityDensityFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-5));
expected = log.LogProbabilityDensityFunction(i);
actual = target.LogProbabilityDensityFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-5));
expected = log.ComplementaryDistributionFunction(i);
actual = target.ComplementaryDistributionFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-5));
double p = log.DistributionFunction(i);
expected = log.InverseDistributionFunction(p);
actual = target.InverseDistributionFunction(p);
Assert.AreEqual(expected, actual, 1e-5);
expected = log.HazardFunction(i);
actual = target.HazardFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-5));
expected = log.CumulativeHazardFunction(i);
actual = target.CumulativeHazardFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-5));
}
}
public void ConstructorTest1()
{
var log = new ShiftedLogLogisticDistribution(location: 0, scale: 0.42, shape: 0.1);
double mean = log.Mean; // 0.069891101544818923
double median = log.Median; // 0.0
double mode = log.Mode; // -0.083441677069328604
double var = log.Variance; // 0.62447259946747213
double cdf = log.DistributionFunction(x: 1.4); // 0.94668863559417671
double pdf = log.ProbabilityDensityFunction(x: 1.4); // 0.090123683626808615
double lpdf = log.LogProbabilityDensityFunction(x: 1.4); // -2.4065722895662613
double ccdf = log.ComplementaryDistributionFunction(x: 1.4); // 0.053311364405823292
double icdf = log.InverseDistributionFunction(p: cdf); // 1.4000000037735139
double hf = log.HazardFunction(x: 1.4); // 1.6905154207038875
double chf = log.CumulativeHazardFunction(x: 1.4); // 2.9316057546685061
string str = log.ToString(CultureInfo.InvariantCulture); // LLD3(x; μ = 0, σ = 0.42, ξ = 0.1)
Assert.AreEqual(0.069891101544818923, mean, 1e-15);
Assert.AreEqual(0.0, median);
Assert.AreEqual(-0.083441677069328604, mode, 1e-15);
Assert.AreEqual(0.62447259946747213, var, 1e-14);
Assert.AreEqual(2.9316057546685061, chf, 1e-15);
Assert.AreEqual(0.94668863559417671, cdf, 1e-15);
Assert.AreEqual(0.090123683626808615, pdf, 1e-15);
Assert.AreEqual(-2.4065722895662613, lpdf, 1e-15);
Assert.AreEqual(1.6905154207038875, hf, 1e-15);
Assert.AreEqual(0.053311364405823292, ccdf, 1e-15);
Assert.AreEqual(1.4000000001930302, icdf, 1e-15);
Assert.AreEqual("LLD3(x; μ = 0, σ = 0.42, ξ = 0.1)", str);
var range1 = log.GetRange(0.95);
var range2 = log.GetRange(0.99);
var range3 = log.GetRange(0.01);
Assert.AreEqual(-1.0712279538154128, range1.Min, 1e-15);
Assert.AreEqual(1.43799453428117, range1.Max, 1e-15);
Assert.AreEqual(-1.5473143609724813, range2.Min, 1e-15);
Assert.AreEqual(2.4498647072756436, range2.Max, 1e-15);
Assert.AreEqual(-1.5473143609724815, range3.Min, 1e-15);
Assert.AreEqual(2.4498647072756436, range3.Max, 1e-15);
}