public void CauchyDistributionConstructorTest2()
{
double location = 0.42;
double scale = 1.57;
CauchyDistribution cauchy = new CauchyDistribution(location, scale);
double mean = cauchy.Mean; // NaN - Cauchy's mean is undefined.
double var = cauchy.Variance; // NaN - Cauchy's variance is undefined.
double median = cauchy.Median; // 0.42
double cdf = cauchy.DistributionFunction(x: 0.27); // 0.46968025841608563
double pdf = cauchy.ProbabilityDensityFunction(x: 0.27); // 0.2009112009763413
double lpdf = cauchy.LogProbabilityDensityFunction(x: 0.27); // -1.6048922547266871
double ccdf = cauchy.ComplementaryDistributionFunction(x: 0.27); // 0.53031974158391437
double icdf = cauchy.InverseDistributionFunction(p: 0.69358638272337991); // 1.5130304686978195
double hf = cauchy.HazardFunction(x: 0.27); // 0.3788491832800277
double chf = cauchy.CumulativeHazardFunction(x: 0.27); // 0.63427516833243092
string str = cauchy.ToString(System.Globalization.CultureInfo.InvariantCulture); // "Cauchy(x; x0 = 0.42, γ = 1.57)
Assert.IsTrue(Double.IsNaN(mean));
Assert.IsTrue(Double.IsNaN(var));
Assert.AreEqual(0.42, median);
Assert.AreEqual(0.63427516833243092, chf);
Assert.AreEqual(0.46968025841608563, cdf);
Assert.AreEqual(0.2009112009763413, pdf);
Assert.AreEqual(-1.6048922547266871, lpdf);
Assert.AreEqual(0.3788491832800277, hf);
Assert.AreEqual(0.53031974158391437, ccdf);
Assert.AreEqual(1.5130304686978195, icdf);
Assert.AreEqual("Cauchy(x; x0 = 0.42, γ = 1.57)", str);
}
public void CauchyDistributionConstructorTest2()
{
double location = 0.42;
double scale = 1.57;
CauchyDistribution cauchy = new CauchyDistribution(location, scale);
double mean = cauchy.Mean; // NaN - Cauchy's mean is undefined.
double var = cauchy.Variance; // NaN - Cauchy's variance is undefined.
double median = cauchy.Median; // 0.42
double mode = cauchy.Mode; // 0.42
double cdf = cauchy.DistributionFunction(x: 0.27); // 0.46968025841608563
double pdf = cauchy.ProbabilityDensityFunction(x: 0.27); // 0.2009112009763413
double lpdf = cauchy.LogProbabilityDensityFunction(x: 0.27); // -1.6048922547266871
double ccdf = cauchy.ComplementaryDistributionFunction(x: 0.27); // 0.53031974158391437
double icdf = cauchy.InverseDistributionFunction(p: 0.69358638272337991); // 1.5130304686978195
double hf = cauchy.HazardFunction(x: 0.27); // 0.3788491832800277
double chf = cauchy.CumulativeHazardFunction(x: 0.27); // 0.63427516833243092
string str = cauchy.ToString(System.Globalization.CultureInfo.InvariantCulture); // "Cauchy(x; x0 = 0.42, γ = 1.57)
Assert.IsTrue(Double.IsNaN(mean));
Assert.IsTrue(Double.IsNaN(var));
Assert.AreEqual(0.42, median);
Assert.AreEqual(0.42, mode, 1e-6);
Assert.AreEqual(0.63427516833243092, chf);
Assert.AreEqual(0.46968025841608563, cdf);
Assert.AreEqual(0.2009112009763413, pdf);
Assert.AreEqual(-1.6048922547266871, lpdf);
Assert.AreEqual(0.3788491832800277, hf);
Assert.AreEqual(0.53031974158391437, ccdf);
Assert.AreEqual(1.5130304686978195, icdf);
Assert.AreEqual("Cauchy(x; x0 = 0.42, γ = 1.57)", str);
var range1 = cauchy.GetRange(0.95);
var range2 = cauchy.GetRange(0.99);
var range3 = cauchy.GetRange(0.01);
Assert.AreEqual(-9.4925897567183526, range1.Min, 1e-10);
Assert.AreEqual(10.332589895085842, range1.Max, 1e-10);
Assert.AreEqual(-49.538210069999685, range2.Min, 1e-10);
Assert.AreEqual(50.378210075966564, range2.Max, 1e-10);
Assert.AreEqual(-49.538210069999892, range3.Min, 1e-10);
Assert.AreEqual(50.378210075966564, range3.Max, 1e-10);
Assert.AreEqual(Double.NegativeInfinity, cauchy.Support.Min);
Assert.AreEqual(Double.PositiveInfinity, cauchy.Support.Max);
Assert.AreEqual(cauchy.InverseDistributionFunction(0), cauchy.Support.Min);
Assert.AreEqual(cauchy.InverseDistributionFunction(1), cauchy.Support.Max);
}
public void LogProbabilityDensityFunctionTest()
{
double[] expected =
{
-3.4572653, -3.2488640, -3.0165321, -2.7541678, -2.4530627, -2.1002413,
-1.6753581, -1.1447299, -0.4515827, 0.4647080, 1.1578552, 0.4647080
};
CauchyDistribution target = new CauchyDistribution(location: 1, scale: 0.1);
for (int i = 0; i < expected.Length; i++)
{
double actual = target.LogProbabilityDensityFunction(i / 10.0);
Assert.AreEqual(expected[i], actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void CauchyDistributionConstructorTest2()
{
double location = 0.42;
double scale = 1.57;
CauchyDistribution cauchy = new CauchyDistribution(location, scale);
double mean = cauchy.Mean; // NaN - Cauchy's mean is undefined.
double var = cauchy.Variance; // NaN - Cauchy's variance is undefined.
double median = cauchy.Median; // 0.42
double cdf = cauchy.DistributionFunction(x: 0.27); // 0.46968025841608563
double pdf = cauchy.ProbabilityDensityFunction(x: 0.27); // 0.2009112009763413
double lpdf = cauchy.LogProbabilityDensityFunction(x: 0.27); // -1.6048922547266871
double ccdf = cauchy.ComplementaryDistributionFunction(x: 0.27); // 0.53031974158391437
double icdf = cauchy.InverseDistributionFunction(p: 0.69358638272337991); // 1.5130304686978195
double hf = cauchy.HazardFunction(x: 0.27); // 0.3788491832800277
double chf = cauchy.CumulativeHazardFunction(x: 0.27); // 0.63427516833243092
string str = cauchy.ToString(System.Globalization.CultureInfo.InvariantCulture); // "Cauchy(x; x0 = 0.42, γ = 1.57)
Assert.IsTrue(Double.IsNaN(mean));
Assert.IsTrue(Double.IsNaN(var));
Assert.AreEqual(0.42, median);
Assert.AreEqual(0.63427516833243092, chf);
Assert.AreEqual(0.46968025841608563, cdf);
Assert.AreEqual(0.2009112009763413, pdf);
Assert.AreEqual(-1.6048922547266871, lpdf);
Assert.AreEqual(0.3788491832800277, hf);
Assert.AreEqual(0.53031974158391437, ccdf);
Assert.AreEqual(1.5130304686978195, icdf);
Assert.AreEqual("Cauchy(x; x0 = 0.42, γ = 1.57)", str);
}
public void LogProbabilityDensityFunctionTest()
{
double[] expected =
{
-3.4572653, -3.2488640, -3.0165321, -2.7541678, -2.4530627, -2.1002413,
-1.6753581, -1.1447299, -0.4515827, 0.4647080, 1.1578552, 0.4647080
};
CauchyDistribution target = new CauchyDistribution(location: 1, scale: 0.1);
for (int i = 0; i < expected.Length; i++)
{
double actual = target.LogProbabilityDensityFunction(i / 10.0);
Assert.AreEqual(expected[i], actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
}
}