public void UniformTest()
{
var target = new TukeyLambdaDistribution(lambda: 1);
var uniform = new UniformContinuousDistribution(-1, +1);
compare(target, uniform, 1e-10);
}
private static void compare(TukeyLambdaDistribution target,
UnivariateContinuousDistribution comparison, double tol)
{
Assert.AreEqual(comparison.Mean, target.Mean);
Assert.AreEqual(comparison.Variance, target.Variance, tol);
Assert.AreEqual(comparison.Entropy, target.Entropy, 1e-4);
Assert.AreEqual(comparison.StandardDeviation, target.StandardDeviation, tol);
Assert.AreEqual(comparison.Mode, target.Mode);
Assert.AreEqual(comparison.Median, target.Median);
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.ProbabilityDensityFunction(x);
double expected = comparison.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, tol);
Assert.IsFalse(Double.IsNaN(actual));
}
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.DistributionFunction(x);
double expected = comparison.DistributionFunction(x);
Assert.AreEqual(expected, actual, tol);
Assert.IsFalse(Double.IsNaN(actual));
}
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.LogProbabilityDensityFunction(x);
double expected = comparison.LogProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, tol);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void LogisticTest()
{
var target = new TukeyLambdaDistribution(lambda: 0);
var logistic = new LogisticDistribution();
compare(target, logistic, 1e-5);
}
public void ConstructorTest()
{
var tukey = new TukeyLambdaDistribution(lambda: 0.14);
double mean = tukey.Mean; // 0.0
double median = tukey.Median; // 0.0
double mode = tukey.Mode; // 0.0
double var = tukey.Variance; // 2.1102970222144855
double stdDev = tukey.StandardDeviation; // 1.4526861402982014
double cdf = tukey.DistributionFunction(x: 1.4); // 0.83252947230217966
double pdf = tukey.ProbabilityDensityFunction(x: 1.4); // 0.17181242109370659
double lpdf = tukey.LogProbabilityDensityFunction(x: 1.4); // -1.7613519723149427
double ccdf = tukey.ComplementaryDistributionFunction(x: 1.4); // 0.16747052769782034
double icdf = tukey.InverseDistributionFunction(p: cdf); // 1.4000000000000004
double hf = tukey.HazardFunction(x: 1.4); // 1.0219566231014163
double chf = tukey.CumulativeHazardFunction(x: 1.4); // 1.7842102556452939
string str = tukey.ToString(CultureInfo.InvariantCulture); // Tukey(x; λ = 0.14)
Assert.AreEqual(0.0, mean);
Assert.AreEqual(0.0, median);
Assert.AreEqual(0.0, mode);
Assert.AreEqual(2.1102970222144855, var);
Assert.AreEqual(1.4526861402982014, stdDev);
Assert.AreEqual(1.7869478972416082, chf);
Assert.AreEqual(0.83252947230217966, cdf);
Assert.AreEqual(0.17181242109370659, pdf);
Assert.AreEqual(-1.7613519723149427, lpdf);
Assert.AreEqual(1.0259263134569006, hf);
Assert.AreEqual(0.16747052769782034, ccdf);
Assert.AreEqual(1.4000000000000004, icdf);
Assert.AreEqual("Tukey(x; λ = 0.14)", str);
var range1 = tukey.GetRange(0.95);
var range2 = tukey.GetRange(0.99);
var range3 = tukey.GetRange(0.01);
Assert.AreEqual(-2.395751074495986, range1.Min);
Assert.AreEqual(2.395751074495986, range1.Max);
Assert.AreEqual(-3.3841891582663117, range2.Min);
Assert.AreEqual(3.3841891582663117, range2.Max);
Assert.AreEqual(-3.3841891582663126, range3.Min);
Assert.AreEqual(3.3841891582663117, range3.Max);
}
