public void fit_gaussian_test()
{
#region doc_fit_gaussian
// Suppose we have the following data, and we would
// like to estimate a distribution from this data
double[][] samples =
{
new double[] { 0, 1 },
new double[] { 1, 2 },
new double[] { 5, 1 },
new double[] { 7, 1 },
new double[] { 6, 1 },
new double[] { 5, 7 },
new double[] { 2, 1 },
};
// Start by specifying a density kernel
IDensityKernel kernel = new GaussianKernel(dimension: 2);
// The density kernel gives a window function centered in a particular sample.
// By creating one of those windows for each sample, we can achieve an empirical
// multivariate distribution function. An output example for a single Gaussian
// kernel would be:
double z = kernel.Function(new double[] { 0, 1 }); // should be 0.096532352630053914
// Create a multivariate Empirical distribution from the samples
var dist = new MultivariateEmpiricalDistribution(kernel, samples);
// Common measures
double[] mean = dist.Mean; // { 3.71, 2.00 }
double[] median = dist.Median; // { 3.71, 2.00 }
double[] var = dist.Variance; // { 7.23, 5.00 } (diagonal from cov)
double[,] cov = dist.Covariance; // { { 7.23, 0.83 }, { 0.83, 5.00 } }
// Probability mass functions
double pdf1 = dist.ProbabilityDensityFunction(new double[] { 2, 1 }); // 0.017657515909330332
double pdf2 = dist.ProbabilityDensityFunction(new double[] { 4, 2 }); // 0.011581172997320841
double pdf3 = dist.ProbabilityDensityFunction(new double[] { 5, 7 }); // 0.0072297668067630525
double lpdf = dist.LogProbabilityDensityFunction(new double[] { 5, 7 }); // -4.929548496891365
#endregion
Assert.AreEqual(0.096532352630053914, z);
Assert.AreEqual(3.7142857142857144, mean[0]);
Assert.AreEqual(2.0, mean[1]);
Assert.AreEqual(3.7142857142857144, median[0]);
Assert.AreEqual(2.0, median[1]);
Assert.AreEqual(7.2380952380952381, var[0]);
Assert.AreEqual(5.0, var[1]);
Assert.AreEqual(7.2380952380952381, cov[0, 0]);
Assert.AreEqual(0.83333333333333337, cov[0, 1]);
Assert.AreEqual(0.83333333333333337, cov[1, 0]);
Assert.AreEqual(5.0, cov[1, 1]);
Assert.AreEqual(0.017657515909330332, pdf1);
Assert.AreEqual(0.011581172997320841, pdf2);
Assert.AreEqual(0.0072297668067630525, pdf3);
Assert.AreEqual(-4.929548496891365, lpdf);
}
public void ConstructorTest4()
{
#region doc_fit_epanechnikov
// Suppose we have the following data, and we would
// like to estimate a distribution from this data
double[][] samples =
{
new double[] { 0, 1 },
new double[] { 1, 2 },
new double[] { 5, 1 },
new double[] { 7, 1 },
new double[] { 6, 1 },
new double[] { 5, 7 },
new double[] { 2, 1 },
};
// Start by specifying a density kernel
IDensityKernel kernel = new EpanechnikovKernel(dimension: 2);
// Create a multivariate Empirical distribution from the samples
var dist = new MultivariateEmpiricalDistribution(kernel, samples);
// Common measures
double[] mean = dist.Mean; // { 3.71, 2.00 }
double[] median = dist.Median; // { 3.71, 2.00 }
double[] var = dist.Variance; // { 7.23, 5.00 } (diagonal from cov)
double[,] cov = dist.Covariance; // { { 7.23, 0.83 }, { 0.83, 5.00 } }
// Probability mass functions
double pdf1 = dist.ProbabilityDensityFunction(new double[] { 2, 1 }); // 0.039131176997318849
double pdf2 = dist.ProbabilityDensityFunction(new double[] { 4, 2 }); // 0.010212109770266639
double pdf3 = dist.ProbabilityDensityFunction(new double[] { 5, 7 }); // 0.02891906722705221
double lpdf = dist.LogProbabilityDensityFunction(new double[] { 5, 7 }); // -3.5432541357714742
#endregion
Assert.AreEqual(3.7142857142857144, mean[0]);
Assert.AreEqual(2.0, mean[1]);
Assert.AreEqual(3.7142857142857144, median[0]);
Assert.AreEqual(2.0, median[1]);
Assert.AreEqual(7.2380952380952381, var[0]);
Assert.AreEqual(5.0, var[1]);
Assert.AreEqual(7.2380952380952381, cov[0, 0]);
Assert.AreEqual(0.83333333333333337, cov[0, 1]);
Assert.AreEqual(0.83333333333333337, cov[1, 0]);
Assert.AreEqual(5.0, cov[1, 1]);
Assert.AreEqual(0.039131176997318849, pdf1);
Assert.AreEqual(0.010212109770266639, pdf2);
Assert.AreEqual(0.02891906722705221, pdf3);
Assert.AreEqual(-3.5432541357714742, lpdf);
}
public void WeightedEmpiricalDistributionConstructorTest2()
{
double[] original = { 5, 5, 1, 4, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 3 };
var distribution = new MultivariateEmpiricalDistribution(original.ToArray());
double[] weights = { 2, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 1 };
double[] source = { 5, 1, 4, 1, 2, 3, 4, 3, 4, 3, 2, 3 };
double[][] samples = source.ToArray();
weights = weights.Divide(weights.Sum());
var target = new MultivariateEmpiricalDistribution(samples,
weights, distribution.Smoothing);
Assert.AreEqual(distribution.Mean[0], target.Mean[0]);
Assert.AreEqual(distribution.Median[0], target.Median[0]);
Assert.AreEqual(distribution.Mode[0], target.Mode[0]);
Assert.AreEqual(distribution.Smoothing[0, 0], target.Smoothing[0, 0]);
Assert.AreEqual(1.3655172413793104, target.Variance[0]);
Assert.AreEqual(target.Weights, weights);
Assert.AreEqual(target.Samples, samples);
for (double x = 0; x < 6; x += 0.1)
{
double actual, expected;
expected = distribution.ComplementaryDistributionFunction(x);
actual = target.ComplementaryDistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.DistributionFunction(x);
actual = target.DistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.LogProbabilityDensityFunction(x);
actual = target.LogProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.ProbabilityDensityFunction(x);
actual = target.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
}
}
public void FitTest()
{
double[] original = { 5, 5, 1, 4, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 3 };
var distribution = new MultivariateEmpiricalDistribution(original.ToJagged());
int[] weights = { 2, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 1 };
double[] sources = { 5, 1, 4, 1, 2, 3, 4, 3, 4, 3, 2, 3 };
double[][] samples = sources.ToJagged();
var target = new MultivariateEmpiricalDistribution(Jagged.Zeros(1, 1));
target.Fit(samples, weights);
Assert.AreEqual(distribution.Mean[0], target.Mean[0]);
Assert.AreEqual(distribution.Median[0], target.Median[0]);
Assert.AreEqual(distribution.Mode[0], target.Mode[0]);
Assert.AreEqual(distribution.Smoothing[0, 0], target.Smoothing[0, 0]);
Assert.AreEqual(distribution.Variance[0], target.Variance[0]);
Assert.IsTrue(target.Weights.IsEqual(weights.Divide(weights.Sum())));
Assert.AreEqual(target.Samples, samples);
for (double x = 0; x < 6; x += 0.1)
{
double actual, expected;
expected = distribution.ComplementaryDistributionFunction(x);
actual = target.ComplementaryDistributionFunction(x);
Assert.AreEqual(expected, actual);
expected = distribution.DistributionFunction(x);
actual = target.DistributionFunction(x);
Assert.AreEqual(expected, actual);
expected = distribution.LogProbabilityDensityFunction(x);
actual = target.LogProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.ProbabilityDensityFunction(x);
actual = target.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
}
}
