IndependentTDistribution Class

[SerializableAttribute]
public class Independent<TDistribution> : MultivariateContinuousDistribution, 
	ISampleableDistribution<double[]>, IDistribution<double[]>, IDistribution, 
	ICloneable, IRandomNumberGenerator<double[]>, IFittableDistribution<double[], IndependentOptions>, 
	IFittable<double[], IndependentOptions>, IFittable<double[]>, 
	IFittableDistribution<double[]>
where TDistribution : IUnivariateDistribution

<SerializableAttribute>
Public Class Independent(Of TDistribution As IUnivariateDistribution)
	Inherits MultivariateContinuousDistribution
	Implements ISampleableDistribution(Of Double()), IDistribution(Of Double()), 
	IDistribution, ICloneable, IRandomNumberGenerator(Of Double()), IFittableDistribution(Of Double(), IndependentOptions), 
	IFittable(Of Double(), IndependentOptions), IFittable(Of Double()), 
	IFittableDistribution(Of Double())

// Declare two normal distributions
NormalDistribution pa = new NormalDistribution(4.2, 1); // p(a)
NormalDistribution pb = new NormalDistribution(7.0, 2); // p(b)

// Now, create a joint distribution combining these two:
var joint = new Independent<NormalDistribution>(pa, pb);

// This distribution assumes the distributions of the two components are independent,
// i.e. if we have 2D input vectors on the form {a, b}, then p({a,b}) = p(a) * p(b). 

// Lets check a simple example. Consider a 2D input vector x = { 4.2, 7.0 } as
// 
double[] x = new double[] { 4.2, 7.0 };

// Those two should be completely equivalent:
double p1 = joint.ProbabilityDensityFunction(x);
double p2 = pa.ProbabilityDensityFunction(x[0]) * pb.ProbabilityDensityFunction(x[1]);

bool equal = p1 == p2; // at this point, equal should be true.

  // Let's consider an input dataset of 2D vectors. We would
  // like to estimate an Independent<NormalDistribution>
  // which best models this data.

 double[][] data =
 {
                 // x, y
     new double[] { 1, 8 },
     new double[] { 2, 6 },
     new double[] { 5, 7 },
     new double[] { 3, 9 },
 };

 // We start by declaring some initial guesses for the
 // distributions of each random variable (x, and y):
 // 
 var distX = new NormalDistribution(0, 1);
 var distY = new NormalDistribution(0, 1);

 // Next, we declare our initial guess Independent distribution
 var joint = new Independent<NormalDistribution>(distX, distY);

 // We can now fit the distribution to our data,
 // producing an estimate of its parameters:
 // 
 joint.Fit(data);

 // At this point, we have estimated our distribution. 

 double[] mean = joint.Mean;     // should be { 2.75,  7.50  }
 double[] var  = joint.Variance; // should be { 2.917, 1.667 } 

                                   //        | 2.917,  0.000 |
 double[,] cov = joint.Covariance; //  Cov = |               |
                                   //        | 0.000,  1.667 |

// The covariance matrix is diagonal, as it would be expected
// if is assumed there are no interactions between components.