/// <summary>
/// Estimates a new Normal distribution from a given set of observations.
/// </summary>
///
public static InverseGaussianDistribution Estimate(double[] observations, double[] weights)
{
var n = new InverseGaussianDistribution();
n.Fit(observations, weights, null);
return(n);
}
public void ConstructorTest2()
{
var invGaussian = new InverseGaussianDistribution(mean: 0.42, shape: 1.2);
double mean = invGaussian.Mean; // 0.42
double median = invGaussian.Median; // 0.35856861093990083
double var = invGaussian.Variance; // 0.061739999999999989
double cdf = invGaussian.DistributionFunction(x: 0.27); // 0.30658791274125458
double pdf = invGaussian.ProbabilityDensityFunction(x: 0.27); // 2.3461495925760354
double lpdf = invGaussian.LogProbabilityDensityFunction(x: 0.27); // 0.85277551314980737
double ccdf = invGaussian.ComplementaryDistributionFunction(x: 0.27); // 0.69341208725874548
double icdf = invGaussian.InverseDistributionFunction(p: cdf); // 0.26999999957543408
double hf = invGaussian.HazardFunction(x: 0.27); // 3.383485283406336
double chf = invGaussian.CumulativeHazardFunction(x: 0.27); // 0.36613081401302111
string str = invGaussian.ToString(CultureInfo.InvariantCulture); // "N^-1(x; μ = 0.42, λ = 1.2)"
Assert.AreEqual(0.42, mean);
Assert.AreEqual(0.35856861093990083, median, 1e-7);
Assert.AreEqual(0.061739999999999989, var);
Assert.AreEqual(0.36613081401302111, chf);
Assert.AreEqual(0.30658791274125458, cdf);
Assert.AreEqual(2.3461495925760354, pdf);
Assert.AreEqual(0.85277551314980737, lpdf);
Assert.AreEqual(3.383485283406336, hf);
Assert.AreEqual(0.69341208725874548, ccdf);
Assert.AreEqual(0.26999999957543408, icdf, 1e-8);
Assert.AreEqual("N^-1(x; μ = 0.42, λ = 1.2)", str);
}
public void ConstructorTest()
{
InverseGaussianDistribution g = new InverseGaussianDistribution(1.2, 4.2);
Assert.AreEqual(1.2, g.Mean);
Assert.AreEqual(4.2, g.Shape);
Assert.AreEqual(0.41142857142857142, g.Variance);
Assert.AreEqual(0.64142698058981851, g.StandardDeviation);
}
public void ConstructorTest2()
{
var invGaussian = new InverseGaussianDistribution(mean: 0.42, shape: 1.2);
double mean = invGaussian.Mean; // 0.42
double median = invGaussian.Median; // 0.35856861093990083
double var = invGaussian.Variance; // 0.061739999999999989
double mode = invGaussian.Mode; // 0.23793654141004067
double cdf = invGaussian.DistributionFunction(x: 0.27); // 0.30658791274125458
double pdf = invGaussian.ProbabilityDensityFunction(x: 0.27); // 2.3461495925760354
double lpdf = invGaussian.LogProbabilityDensityFunction(x: 0.27); // 0.85277551314980737
double ccdf = invGaussian.ComplementaryDistributionFunction(x: 0.27); // 0.69341208725874548
double icdf = invGaussian.InverseDistributionFunction(p: cdf); // 0.26999999957543408
double hf = invGaussian.HazardFunction(x: 0.27); // 3.383485283406336
double chf = invGaussian.CumulativeHazardFunction(x: 0.27); // 0.36613081401302111
string str = invGaussian.ToString(CultureInfo.InvariantCulture); // "N^-1(x; μ = 0.42, λ = 1.2)"
Assert.AreEqual(0.42, mean);
Assert.AreEqual(0.35856861093990083, median, 1e-6);
Assert.AreEqual(0.061739999999999989, var);
Assert.AreEqual(0.36613081401302111, chf);
Assert.AreEqual(0.23793654141004067, mode);
Assert.AreEqual(0.30658791274125458, cdf);
Assert.AreEqual(2.3461495925760354, pdf);
Assert.AreEqual(0.85277551314980737, lpdf);
Assert.AreEqual(3.383485283406336, hf);
Assert.AreEqual(0.69341208725874548, ccdf);
Assert.AreEqual(0.26999999957543408, icdf, 1e-7);
Assert.AreEqual("N^-1(x; μ = 0.42, λ = 1.2)", str);
var range1 = invGaussian.GetRange(0.95);
var range2 = invGaussian.GetRange(0.99);
var range3 = invGaussian.GetRange(0.01);
Assert.AreEqual(0.14769446268576839, range1.Min);
Assert.AreEqual(0.90166590229504751, range1.Max);
Assert.AreEqual(0.10646291322190742, range2.Min);
Assert.AreEqual(1.2855706686397079, range2.Max);
Assert.AreEqual(0.10646291322190739, range3.Min);
Assert.AreEqual(1.2855706686397079, range3.Max);
}
public void ProbabilityFunctionTest2()
{
InverseGaussianDistribution g = new InverseGaussianDistribution(4.1, 1.2);
double[] expected =
{
0.0457398, 0.323655, 0.477189, 0.509189, 0.490063, 0.453721, 0.413867, 0.375711, 0.34101, 0.310123
};
for (int i = 0; i < expected.Length; i++)
{
double x = (i + 1) / 10.0;
double actual = g.ProbabilityDensityFunction(x);
Assert.AreEqual(expected[i], actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
}
public void ProbabilityFunctionTest()
{
InverseGaussianDistribution g = new InverseGaussianDistribution(1.2, 4.2);
double expected = 0.363257;
double actual = g.ProbabilityDensityFunction(0.42);
Assert.AreEqual(expected, actual, 1e-6);
}
public void CumulativeFunctionTest2()
{
InverseGaussianDistribution g = new InverseGaussianDistribution(4.1, 1.2);
double[] expected =
{
0.000710666, 0.0190607, 0.0604859, 0.110461, 0.160665, 0.207921, 0.2513, 0.290755, 0.326559, 0.359084
};
for (int i = 0; i < expected.Length; i++)
{
double x = (i + 1) / 10.0;
double actual = g.DistributionFunction(x);
Assert.AreEqual(expected[i], actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
}
public void CumulativeFunctionTest()
{
InverseGaussianDistribution g = new InverseGaussianDistribution(1.2, 4.2);
double expected = 0.030679;
double actual = g.DistributionFunction(0.42);
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
public void ConstructorTest4()
{
var original = new InverseGaussianDistribution(mean: 0.42, shape: 1.2);
var invGaussian = GeneralContinuousDistribution.FromDistributionFunction(
original.Support, original.DistributionFunction);
testInvGaussian(invGaussian);
}
public void ConstructorTest3()
{
var original = new InverseGaussianDistribution(mean: 0.42, shape: 1.2);
var invGaussian = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.DistributionFunction(i);
double actual = invGaussian.DistributionFunction(i);
double diff = Math.Abs(expected - actual);
Assert.AreEqual(expected, actual, 0.1);
}
testInvGaussian(invGaussian);
}
public void GenerateTest4()
{
Accord.Math.Random.Generator.Seed = 0;
InverseGaussianDistribution target = new InverseGaussianDistribution(0.4, 0.2);
double[] samples = new double[10000000];
for (int i = 0; i < samples.Length; i++)
samples[i] = target.Generate();
var actual = InverseGaussianDistribution.Estimate(samples);
actual.Fit(samples);
Assert.AreEqual(0.4, actual.Mean, 1e-3);
Assert.AreEqual(0.2, actual.Shape, 1e-3);
}
public void GenerateTest2()
{
Accord.Math.Tools.SetupGenerator(0);
InverseGaussianDistribution target = new InverseGaussianDistribution(5, 2);
double[] samples = target.Generate(10000000);
var actual = InverseGaussianDistribution.Estimate(samples);
actual.Fit(samples);
Assert.AreEqual(5, actual.Mean, 1e-3);
Assert.AreEqual(2, actual.Shape, 1e-3);
}
public void GenerateTest()
{
InverseGaussianDistribution target = new InverseGaussianDistribution(1, 1);
double[] samples = target.Generate(1000000);
InverseGaussianDistribution actual = new InverseGaussianDistribution(5, 5);
actual.Fit(samples);
Assert.AreEqual(1, actual.Mean, 0.01);
Assert.AreEqual(1, actual.Shape, 0.01);
}
public void MedianTest()
{
InverseGaussianDistribution target = new InverseGaussianDistribution(6, 2);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void GenerateTest3()
{
InverseGaussianDistribution target = new InverseGaussianDistribution(4, 2);
double[] samples = new double[1000000];
for (int i = 0; i < samples.Length; i++)
samples[i] = target.Generate();
var actual = InverseGaussianDistribution.Estimate(samples);
actual.Fit(samples);
Assert.AreEqual(4, actual.Mean, 0.01);
Assert.AreEqual(2, actual.Shape, 0.01);
}
public void GenerateTest2()
{
InverseGaussianDistribution target = new InverseGaussianDistribution(5, 2);
double[] samples = target.Generate(1000000);
var actual = InverseGaussianDistribution.Estimate(samples);
actual.Fit(samples);
Assert.AreEqual(5, actual.Mean, 0.01);
Assert.AreEqual(2, actual.Shape, 0.01);
}
