public void ConstructorTest()
{
var vonMises = new VonMisesDistribution(mean: 0.42, concentration: 1.2);
double mean = vonMises.Mean; // 0.42
double median = vonMises.Median; // 0.42
double var = vonMises.Variance; // 0.48721760532782921
double cdf = vonMises.DistributionFunction(x: 1.4); // 0.81326928491589345
double pdf = vonMises.ProbabilityDensityFunction(x: 1.4); // 0.2228112141141676
double lpdf = vonMises.LogProbabilityDensityFunction(x: 1.4); // -1.5014304395467863
double ccdf = vonMises.ComplementaryDistributionFunction(x: 1.4); // 0.18673071508410655
double icdf = vonMises.InverseDistributionFunction(p: cdf); // 1.3999999637927665
double hf = vonMises.HazardFunction(x: 1.4); // 1.1932220899695576
double chf = vonMises.CumulativeHazardFunction(x: 1.4); // 1.6780877262500649
string str = vonMises.ToString(CultureInfo.InvariantCulture); // VonMises(x; μ = 0.42, κ = 1.2)
double imedian = vonMises.InverseDistributionFunction(p: 0.5);
Assert.AreEqual(0.42, mean);
Assert.AreEqual(0.42, median);
Assert.AreEqual(0.42000000260613551, imedian, 1e-8);
Assert.AreEqual(0.48721760532782921, var);
Assert.AreEqual(1.6780877262500649, chf);
Assert.AreEqual(0.81326928491589345, cdf);
Assert.AreEqual(0.2228112141141676, pdf);
Assert.AreEqual(-1.5014304395467863, lpdf);
Assert.AreEqual(1.1932220899695576, hf);
Assert.AreEqual(0.18673071508410655, ccdf);
Assert.AreEqual(1.39999999999, icdf, 1e-8);
Assert.AreEqual("VonMises(x; μ = 0.42, κ = 1.2)", str);
}
public void ProbabilityDensityFunctionTest()
{
VonMisesDistribution dist = new VonMisesDistribution(2.249981, 2.411822);
double actual = dist.ProbabilityDensityFunction(2.14);
double expected = 0.5686769438969197;
Assert.AreEqual(expected, actual, 1e-10);
}
public void ConstructorTest16()
{
var original = new VonMisesDistribution(mean: 0.42, concentration: 1.2);
var vonMises = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
testVonMises(vonMises, 100);
}
public void ConstructorTest17()
{
var original = new VonMisesDistribution(mean: 0.42, concentration: 1.2);
var vonMises = GeneralContinuousDistribution.FromDistributionFunction(
original.Support, original.DistributionFunction);
testVonMises(vonMises);
}
public void LogProbabilityDensityFunctionTest()
{
VonMisesDistribution dist = new VonMisesDistribution(2.249981, 2.411822);
double x = 2.14;
double actual = dist.LogProbabilityDensityFunction(x);
double expected = System.Math.Log(dist.ProbabilityDensityFunction(x));
Assert.AreEqual(expected, actual, 1e-10);
}
public void ConstructorTest()
{
var vonMises = new VonMisesDistribution(mean: 0.42, concentration: 1.2);
double mean = vonMises.Mean; // 0.42
double median = vonMises.Median; // 0.42
double var = vonMises.Variance; // 0.48721760532782921
double mode = vonMises.Mode; // 0.42
double cdf = vonMises.DistributionFunction(x: 1.4); // 0.81326928491589345
double pdf = vonMises.ProbabilityDensityFunction(x: 1.4); // 0.2228112141141676
double lpdf = vonMises.LogProbabilityDensityFunction(x: 1.4); // -1.5014304395467863
double ccdf = vonMises.ComplementaryDistributionFunction(x: 1.4); // 0.18673071508410655
double icdf = vonMises.InverseDistributionFunction(p: cdf); // 1.3999999637927665
double hf = vonMises.HazardFunction(x: 1.4); // 1.1932220899695576
double chf = vonMises.CumulativeHazardFunction(x: 1.4); // 1.6780877262500649
string str = vonMises.ToString(CultureInfo.InvariantCulture); // VonMises(x; μ = 0.42, κ = 1.2)
double imedian = vonMises.InverseDistributionFunction(p: 0.5);
Assert.AreEqual(0.42, mean);
Assert.AreEqual(0.42, median);
Assert.AreEqual(0.42, mode);
Assert.AreEqual(0.42000000260613551, imedian, 1e-8);
Assert.AreEqual(0.48721760532782921, var);
Assert.AreEqual(1.6780877262500649, chf);
Assert.AreEqual(0.81326928491589345, cdf);
Assert.AreEqual(0.2228112141141676, pdf);
Assert.AreEqual(-1.5014304395467863, lpdf);
Assert.AreEqual(1.1932220899695576, hf);
Assert.AreEqual(0.18673071508410655, ccdf);
Assert.AreEqual(1.39999999999, icdf, 1e-8);
Assert.AreEqual("VonMises(x; μ = 0.42, κ = 1.2)", str);
var range1 = vonMises.GetRange(0.95);
var range2 = vonMises.GetRange(0.99);
var range3 = vonMises.GetRange(0.01);
Assert.AreEqual(-1.5990672124935188, range1.Min, 1e-14);
Assert.AreEqual(2.4390672124935207, range1.Max, 1e-14);
Assert.AreEqual(-2.4355782410688764, range2.Min, 1e-14);
Assert.AreEqual(3.2755782410688861, range2.Max, 1e-14);
Assert.AreEqual(-2.4355782410688764, range3.Min, 1e-14);
Assert.AreEqual(3.2755782410688861, range3.Max, 1e-14);
Assert.AreEqual(-2.7215926535897932, vonMises.Support.Min, 1e-10);
Assert.AreEqual(3.561592653589793, vonMises.Support.Max, 1e-10);
Assert.AreEqual(vonMises.InverseDistributionFunction(0), vonMises.Support.Min);
Assert.AreEqual(vonMises.InverseDistributionFunction(1), vonMises.Support.Max);
}
public void generate_test()
{
double kappa = 35;
var vm = new VonMisesDistribution(0, kappa);
var target = new VonMisesFisherDistribution(new double[] { -1, 0, 0 }, kappa);
double[][] actual = target.Generate(100);
var sphere = new UniformSphereDistribution(3);
for (int i = 0; i < actual.Length; i++)
{
double p = sphere.ProbabilityDensityFunction(actual[i]);
Assert.AreEqual(0.025330295910584444, p, 1e-8);
}
}
public void FitTest()
{
double[] angles =
{
2.537498, 0.780449, 3.246623, 1.835845, 1.525273,
2.821987, 1.783134, 1.165753, 3.298262, 2.941366,
2.485515, 2.090029, 2.460631, 2.804243, 1.626327,
};
var distribution = VonMisesDistribution.Estimate(angles);
Assert.AreEqual(2.411822, distribution.Concentration, 1e-6);
Assert.AreEqual(2.249981, distribution.Mean, 1e-6);
Assert.AreEqual(0.2441525, distribution.Variance, 1e-3);
}
public void ConstructorTest17()
{
var original = new VonMisesDistribution(mean: 0.42, concentration: 1.2);
var vonMises = GeneralContinuousDistribution.FromDistributionFunction(
original.Support, original.DistributionFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.ProbabilityDensityFunction(i);
double actual = vonMises.ProbabilityDensityFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-4));
}
testVonMises(vonMises, 1);
}
public void ConstructorTest1()
{
// If p=2 the distribution reduces to the von Mises distribution on the circle.
double kappa = 4.2;
var vm = new VonMisesDistribution(0, kappa);
var target = new VonMisesFisherDistribution(new double[] { -1, 0 }, kappa);
double s = Math.Sqrt(2) / 2;
double[] mean = target.Mean;
double a000 = target.ProbabilityDensityFunction(new double[] { +1, +0 });
double a045 = target.ProbabilityDensityFunction(new double[] { +s, +s });
double a090 = target.ProbabilityDensityFunction(new double[] { +0, +1 });
double a135 = target.ProbabilityDensityFunction(new double[] { -s, +s });
double a180 = target.ProbabilityDensityFunction(new double[] { -1, +0 });
double a225 = target.ProbabilityDensityFunction(new double[] { -s, -s });
double a270 = target.ProbabilityDensityFunction(new double[] { +0, -1 });
double a315 = target.ProbabilityDensityFunction(new double[] { +s, -s });
double a360 = target.ProbabilityDensityFunction(new double[] { +1, +0 });
double offset = -Math.PI;
double e000 = vm.ProbabilityDensityFunction(offset + 0);
double e045 = vm.ProbabilityDensityFunction(offset + Math.PI / 4);
double e090 = vm.ProbabilityDensityFunction(offset + Math.PI / 2);
double e135 = vm.ProbabilityDensityFunction(offset + Math.PI * (3 / 4.0));
double e180 = vm.ProbabilityDensityFunction(offset + Math.PI);
double e225 = vm.ProbabilityDensityFunction(offset + Math.PI * (5 / 4.0));
double e270 = vm.ProbabilityDensityFunction(offset + Math.PI * (3 / 2.0));
double e315 = vm.ProbabilityDensityFunction(offset + Math.PI * (7 / 4.0));
double e360 = vm.ProbabilityDensityFunction(offset + Math.PI * 2);
Assert.AreEqual(e000, a000, 1e-8);
Assert.AreEqual(e045, a045, 1e-8);
Assert.AreEqual(e090, a090, 1e-8);
Assert.AreEqual(e135, a135, 1e-8);
Assert.AreEqual(e180, a180, 1e-8);
Assert.AreEqual(e225, a225, 1e-8);
Assert.AreEqual(e270, a270, 1e-8);
Assert.AreEqual(e315, a315, 1e-8);
Assert.AreEqual(e360, a360, 1e-8);
}
public void MedianTest()
{
VonMisesDistribution target = new VonMisesDistribution(1.621, 4.52);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5), 1e-6);
}