GaussianKernel Class

[SerializableAttribute]
public class GaussianKernel : IRadiallySymmetricKernel, 
	IDensityKernel

<SerializableAttribute>
Public Class GaussianKernel
	Implements IRadiallySymmetricKernel, IDensityKernel

// 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