private static void test(GeneralizedNormalDistribution target, UnivariateContinuousDistribution normal)
{
Assert.AreEqual(normal.Mean, target.Mean);
Assert.AreEqual(normal.Variance, target.Variance, 1e-10);
Assert.AreEqual(normal.Entropy, target.Entropy, 1e-10);
Assert.AreEqual(normal.StandardDeviation, target.StandardDeviation, 1e-10);
Assert.AreEqual(normal.Mode, target.Mode);
Assert.AreEqual(normal.Median, target.Median);
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.ProbabilityDensityFunction(x);
double expected = normal.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
Assert.IsFalse(Double.IsNaN(actual));
}
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.LogProbabilityDensityFunction(x);
double expected = normal.LogProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void NormalTest()
{
var target = GeneralizedNormalDistribution.Normal(mean: 0.42, stdDev: 4.2);
var normal = new NormalDistribution(mean: 0.42, stdDev: 4.2);
test(target, normal);
}
public void LaplaceTest()
{
var target = GeneralizedNormalDistribution.Laplace(location: 0.42, scale: 4.2);
var normal = new LaplaceDistribution(location: 0.42, scale: 4.2);
test(target, normal);
}
public void ConstructorTest1()
{
var normal = new GeneralizedNormalDistribution(location: 1, scale: 5, shape: 0.42);
double mean = normal.Mean; // 1
double median = normal.Median; // 1
double mode = normal.Mode; // 1
double var = normal.Variance; // 19200.781700666659
double cdf = normal.DistributionFunction(x: 1.4); // 0.50877105447218995
double pdf = normal.ProbabilityDensityFunction(x: 1.4); // 0.024215092283124507
double lpdf = normal.LogProbabilityDensityFunction(x: 1.4); // -3.7207791921441378
double ccdf = normal.ComplementaryDistributionFunction(x: 1.4); // 0.49122894552781005
double icdf = normal.InverseDistributionFunction(p: cdf); // 1.4000000149740104
double hf = normal.HazardFunction(x: 1.4); // 0.049294921448706883
double chf = normal.CumulativeHazardFunction(x: 1.4); // 0.71084497569360638
string str = normal.ToString(CultureInfo.InvariantCulture); // GGD(x; μ = 1, α = 5, β = 0.42)
Assert.AreEqual(1, mean);
Assert.AreEqual(1, median);
Assert.AreEqual(1, mode);
Assert.AreEqual(19200.781700666659, var);
Assert.AreEqual(0.71084497569360638, chf);
Assert.AreEqual(0.50877105447218995, cdf);
Assert.AreEqual(0.024215092283124507, pdf);
Assert.AreEqual(-3.7207791921441378, lpdf);
Assert.AreEqual(0.049294921448706883, hf);
Assert.AreEqual(0.49122894552781005, ccdf);
Assert.AreEqual(1.4000000149740104, icdf);
Assert.AreEqual("GGD(x; μ = 1, α = 5, β = 0.42)", str);
}
public void SupportTest1()
{
var target = new GeneralizedNormalDistribution(0.0, 10, 2);
var range = target.Support;
Assert.AreEqual(double.NegativeInfinity, range.Min);
Assert.AreEqual(double.PositiveInfinity, range.Max);
}
public void DistributionFunctionTest2()
{
var target = GeneralizedNormalDistribution.Laplace(location: 0.42, scale: 4.2);
var normal = new LaplaceDistribution(location: 0.42, scale: 4.2);
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.DistributionFunction(x);
double expected = normal.DistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void DistributionFunctionTest1()
{
var target = GeneralizedNormalDistribution.Normal(mean: 0.42, stdDev: 4.2);
var normal = new NormalDistribution(mean: 0.42, stdDev: 4.2);
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.DistributionFunction(x);
double expected = normal.DistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void ConstructorTest1()
{
var normal = new GeneralizedNormalDistribution(location: 1, scale: 5, shape: 0.42);
double mean = normal.Mean; // 1
double median = normal.Median; // 1
double mode = normal.Mode; // 1
double var = normal.Variance; // 19200.781700666659
double cdf = normal.DistributionFunction(x: 1.4); // 0.51076148867681703
double pdf = normal.ProbabilityDensityFunction(x: 1.4); // 0.024215092283124507
double lpdf = normal.LogProbabilityDensityFunction(x: 1.4); // -3.7207791921441378
double ccdf = normal.ComplementaryDistributionFunction(x: 1.4); // 0.48923851132318297
double icdf = normal.InverseDistributionFunction(p: cdf); // 1.4000000149740108
double hf = normal.HazardFunction(x: 1.4); // 0.049495474543966168
double chf = normal.CumulativeHazardFunction(x: 1.4); // 0.7149051552030572
string str = normal.ToString(CultureInfo.InvariantCulture); // GGD(x; μ = 1, α = 5, β = 0.42)
Assert.AreEqual(1, mean);
Assert.AreEqual(1, median);
Assert.AreEqual(1, mode);
Assert.AreEqual(19200.781700666659, var);
Assert.AreEqual(0.7149051552030572, chf);
Assert.AreEqual(0.51076148867681703, cdf);
Assert.AreEqual(0.024215092283124507, pdf);
Assert.AreEqual(-3.7207791921441378, lpdf);
Assert.AreEqual(0.049495474543966168, hf);
Assert.AreEqual(0.48923851132318297, ccdf);
Assert.AreEqual(1.4000000149740108, icdf);
Assert.AreEqual("GGD(x; μ = 1, α = 5, β = 0.42)", str);
var range1 = normal.GetRange(0.95);
var range2 = normal.GetRange(0.99);
var range3 = normal.GetRange(0.01);
Assert.AreEqual(-173.60070095277663, range1.Min);
Assert.AreEqual(175.60070093821949, range1.Max);
Assert.AreEqual(-428.92857248354409, range2.Min);
Assert.AreEqual(430.92857248354375, range2.Max);
Assert.AreEqual(-428.92857248354403, range3.Min);
Assert.AreEqual(430.92857248354375, range3.Max);
Assert.AreEqual(double.NegativeInfinity, normal.Support.Min);
Assert.AreEqual(double.PositiveInfinity, normal.Support.Max);
Assert.AreEqual(normal.InverseDistributionFunction(0), normal.Support.Min);
Assert.AreEqual(normal.InverseDistributionFunction(1), normal.Support.Max);
}
public void NormalTest2()
{
var target = GeneralizedNormalDistribution.Normal(mean: 0.0, stdDev: 2 / Constants.Sqrt2);
var normal = new NormalDistribution(mean: 0.0, stdDev: 2 / Constants.Sqrt2);
test(target, normal);
var support = target.Support;
Assert.AreEqual(normal.Support.Min, support.Min);
Assert.AreEqual(normal.Support.Max, support.Max);
for (double i = 0.01; i <= 1; i += 0.01)
{
var actual = normal.GetRange(i);
var expected = normal.GetRange(i);
Assert.AreEqual(expected.Min, actual.Min);
Assert.AreEqual(expected.Max, actual.Max);
}
}
public void LaplaceTest()
{
var target = GeneralizedNormalDistribution.Laplace(location: 0.42, scale: 4.2);
var normal = new LaplaceDistribution(location: 0.42, scale: 4.2);
test(target, normal);
var support = target.Support;
Assert.AreEqual(normal.Support.Min, support.Min);
Assert.AreEqual(normal.Support.Max, support.Max);
for (double i = 0.01; i <= 1.0; i += 0.01)
{
var actual = normal.GetRange(i);
var expected = normal.GetRange(i);
Assert.AreEqual(expected.Min, actual.Min);
Assert.AreEqual(expected.Max, actual.Max);
}
}
