/// <summary>
/// Estimates a new Nakagami distribution from a given set of observations.
/// </summary>
///
public static NakagamiDistribution Estimate(double[] observations, double[] weights)
{
var n = new NakagamiDistribution();
n.Fit(observations, weights, null);
return(n);
}
public void ConstructorTest2()
{
var nakagami = new NakagamiDistribution(shape: 2.4, spread: 4.2);
double mean = nakagami.Mean; // 1.946082119049118
double median = nakagami.Median; // 1.9061151110206338
double var = nakagami.Variance; // 0.41276438591729486
double cdf = nakagami.DistributionFunction(x: 1.4); // 0.20603416752368109
double pdf = nakagami.ProbabilityDensityFunction(x: 1.4); // 0.49253215371343023
double lpdf = nakagami.LogProbabilityDensityFunction(x: 1.4); // -0.708195533773302
double ccdf = nakagami.ComplementaryDistributionFunction(x: 1.4); // 0.79396583247631891
double icdf = nakagami.InverseDistributionFunction(p: cdf); // 1.400000000131993
double hf = nakagami.HazardFunction(x: 1.4); // 0.62034426869133652
double chf = nakagami.CumulativeHazardFunction(x: 1.4); // 0.23071485080660473
string str = nakagami.ToString(CultureInfo.InvariantCulture); // Nakagami(x; μ = 2,4, ω = 4,2)"
Assert.AreEqual(1.946082119049118, mean);
Assert.AreEqual(1.9061151110206338, median, 1e-6);
Assert.AreEqual(0.41276438591729486, var);
Assert.AreEqual(0.23071485080660473, chf);
Assert.AreEqual(0.20603416752368109, cdf);
Assert.AreEqual(0.49253215371343023, pdf);
Assert.AreEqual(-0.708195533773302, lpdf);
Assert.AreEqual(0.62034426869133652, hf);
Assert.AreEqual(0.79396583247631891, ccdf);
Assert.AreEqual(1.40, icdf, 1e-7);
Assert.AreEqual("Nakagami(x; μ = 2.4, ω = 4.2)", str);
}
public void ConstructorTest2()
{
var nakagami = new NakagamiDistribution(shape: 2.4, spread: 4.2);
double mean = nakagami.Mean; // 1.946082119049118
double median = nakagami.Median; // 1.9061151110206338
double var = nakagami.Variance; // 0.41276438591729486
double mode = nakagami.Mode; // 1.8234582528810468
double cdf = nakagami.DistributionFunction(x: 1.4); // 0.20603416752368109
double pdf = nakagami.ProbabilityDensityFunction(x: 1.4); // 0.49253215371343023
double lpdf = nakagami.LogProbabilityDensityFunction(x: 1.4); // -0.708195533773302
double ccdf = nakagami.ComplementaryDistributionFunction(x: 1.4); // 0.79396583247631891
double icdf = nakagami.InverseDistributionFunction(p: cdf); // 1.400000000131993
double hf = nakagami.HazardFunction(x: 1.4); // 0.62034426869133652
double chf = nakagami.CumulativeHazardFunction(x: 1.4); // 0.23071485080660473
string str = nakagami.ToString(CultureInfo.InvariantCulture); // Nakagami(x; μ = 2,4, ω = 4,2)"
Assert.AreEqual(1.946082119049118, mean);
Assert.AreEqual(1.9061151110206338, median, 1e-6);
Assert.AreEqual(1.8234582528810468, mode);
Assert.AreEqual(0.41276438591729486, var);
Assert.AreEqual(0.23071485080660473, chf);
Assert.AreEqual(0.20603416752368109, cdf);
Assert.AreEqual(0.49253215371343023, pdf);
Assert.AreEqual(-0.708195533773302, lpdf);
Assert.AreEqual(0.62034426869133652, hf);
Assert.AreEqual(0.79396583247631891, ccdf);
Assert.AreEqual(1.40, icdf, 1e-7);
Assert.AreEqual("Nakagami(x; μ = 2.4, ω = 4.2)", str);
var range1 = nakagami.GetRange(0.95);
var range2 = nakagami.GetRange(0.99);
var range3 = nakagami.GetRange(0.01);
Assert.AreEqual(0.96015082529305074, range1.Min);
Assert.AreEqual(3.0683231810919338, range1.Max);
Assert.AreEqual(0.65984207711153242, range2.Min);
Assert.AreEqual(3.5903316858157317, range2.Max);
Assert.AreEqual(0.6598420771115322, range3.Min);
Assert.AreEqual(3.5903316858157317, range3.Max);
}
public void ConstructorTest()
{
NakagamiDistribution n = new NakagamiDistribution(0.807602, 12.5);
Assert.AreEqual(3.0510602824983368, n.Mean);
Assert.AreEqual(3.1910311525611705, n.Variance);
}
public void MedianTest()
{
NakagamiDistribution target = new NakagamiDistribution(5.42, 1.37);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void GenerateTest2()
{
Accord.Math.Tools.SetupGenerator(0);
NakagamiDistribution target = new NakagamiDistribution(4, 2);
double[] samples = new double[1000000];
for (int i = 0; i < samples.Length; i++)
samples[i] = target.Generate();
var actual = NakagamiDistribution.Estimate(samples);
actual.Fit(samples);
Assert.AreEqual(4, actual.Shape, 0.01);
Assert.AreEqual(2, actual.Spread, 0.01);
}
public void GenerateTest()
{
NakagamiDistribution target = new NakagamiDistribution(2, 5);
double[] samples = target.Generate(1000000);
var actual = NakagamiDistribution.Estimate(samples);
actual.Fit(samples);
Assert.AreEqual(2, actual.Shape, 0.01);
Assert.AreEqual(5, actual.Spread, 0.01);
}
public void CumulativeDistributionTest()
{
NakagamiDistribution n = new NakagamiDistribution(0.807602, 12.5);
double[] expected = { 0, 0.1139332, 0.3209643, 0.541133, 0.7258253, 0.8551455 };
double[] actual = new double[expected.Length];
for (int i = 0; i < actual.Length; i++)
actual[i] = n.DistributionFunction(i);
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 1e-6);
Assert.IsFalse(double.IsNaN(actual[i]));
}
}
public void ProbabilityDistributionTest()
{
NakagamiDistribution n = new NakagamiDistribution(0.807602, 12.5);
double[] expected = { 0, 0.1775314, 0.224023, 0.2081279, 0.158044, 0.101360 };
double[] actual = new double[expected.Length];
for (int i = 0; i < actual.Length; i++)
actual[i] = n.ProbabilityDensityFunction(i);
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 1e-5);
Assert.IsFalse(double.IsNaN(actual[i]));
}
}
public void ConstructorTest15()
{
var original = new NakagamiDistribution(shape: 2.4, spread: 4.2);
var nakagami = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.DistributionFunction(i);
double actual = nakagami.DistributionFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-2));
Assert.IsFalse(double.IsNaN(expected));
Assert.IsFalse(double.IsNaN(actual));
}
testNakagami(nakagami);
}
public void ConstructorTest14()
{
var original = new NakagamiDistribution(shape: 2.4, spread: 4.2);
var nakagami = GeneralContinuousDistribution.FromDistributionFunction(
original.Support, original.DistributionFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.ProbabilityDensityFunction(i);
double actual = nakagami.ProbabilityDensityFunction(i);
double diff = Math.Abs(expected - actual);
Assert.AreEqual(expected, actual, 1e-3);
Assert.IsFalse(double.IsNaN(expected));
Assert.IsFalse(double.IsNaN(actual));
}
testNakagami(nakagami);
}
public void ConstructorTest15()
{
var original = new NakagamiDistribution(shape: 2.4, spread: 4.2);
var nakagami = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
testNakagami(nakagami);
}
