MultivariateNormalDistribution Class

[SerializableAttribute]
public class MultivariateNormalDistribution : MultivariateContinuousDistribution, 
	IFittableDistribution<double[], NormalOptions>, IFittable<double[], NormalOptions>, 
	IFittable<double[]>, IFittableDistribution<double[]>, IDistribution<double[]>, 
	IDistribution, ICloneable, ISampleableDistribution<double[]>, IRandomNumberGenerator<double[]>

<SerializableAttribute>
Public Class MultivariateNormalDistribution
	Inherits MultivariateContinuousDistribution
	Implements IFittableDistribution(Of Double(), NormalOptions), 
	IFittable(Of Double(), NormalOptions), IFittable(Of Double()), 
	IFittableDistribution(Of Double()), IDistribution(Of Double()), 
	IDistribution, ICloneable, ISampleableDistribution(Of Double()), IRandomNumberGenerator(Of Double())

// Create a multivariate Gaussian distribution 
var dist = new MultivariateNormalDistribution(

    // mean vector mu
    mean: new double[] 
    {
        4, 2 
    },

    // covariance matrix sigma
    covariance: new double[,] 
    {
        { 0.3, 0.1 },
        { 0.1, 0.7 }
    }
);

// Common measures
double[] mean = dist.Mean;     // { 4, 2 }
double[] median = dist.Median; // { 4, 2 }
double[] var = dist.Variance;  // { 0.3, 0.7 } (diagonal from cov)
double[,] cov = dist.Covariance; // { { 0.3, 0.1 }, { 0.1, 0.7 } }

// Probability mass functions
double pdf1 = dist.ProbabilityDensityFunction(new double[] { 2, 5 }); // 0.000000018917884164743237
double pdf2 = dist.ProbabilityDensityFunction(new double[] { 4, 2 }); // 0.35588127170858852
double pdf3 = dist.ProbabilityDensityFunction(new double[] { 3, 7 }); // 0.000000000036520107734505265
double lpdf = dist.LogProbabilityDensityFunction(new double[] { 3, 7 }); // -24.033158110192296

// Cumulative distribution function (for up to two dimensions)
double cdf = dist.DistributionFunction(new double[] { 3, 5 }); // 0.033944035782101548

// Generate samples from this distribution:
double[][] sample = dist.Generate(1000000);

double[][] observations = 
{
    new double[] { 1, 2 },
    new double[] { 1, 2 },
    new double[] { 1, 2 },
    new double[] { 1, 2 }
};

// Create a multivariate Gaussian for 2 dimensions
var normal = new MultivariateNormalDistribution(2);

// Specify a regularization constant in the fitting options
NormalOptions options = new NormalOptions() { Regularization = double.Epsilon };

// Fit the distribution to the data
normal.Fit(observations, options);

// Check distribution parameters
double[] mean = normal.Mean;     // { 1, 2 }
double[] var  = normal.Variance; // { 4.9E-324, 4.9E-324 } (almost machine zero)

// Create a new Excel reader to read data from a spreadsheet
ExcelReader reader = new ExcelReader(@"test.xls", hasHeaders: false);

// Extract the "Data" worksheet from the xls
DataTable table = reader.GetWorksheet("Data");

// Convert the data table to a jagged matrix
double[][] observations = table.ToArray();


// Estimate a new Multivariate Normal Distribution from the observations
var dist = MultivariateNormalDistribution.Estimate(observations, new NormalOptions()
{
    Regularization = 1e-10 // this value will be added to the diagonal until it becomes positive-definite
});