MixtureT Class

[SerializableAttribute]
public class Mixture<T> : UnivariateContinuousDistribution, IMixture<T>, 
	IDistribution, ICloneable, IFittableDistribution<double, MixtureOptions>, 
	IFittable<double, MixtureOptions>, IFittable<double>, 
	IFittableDistribution<double>, IDistribution<double>, ISampleableDistribution<double>, 
	IRandomNumberGenerator<double>
where T : Object, IUnivariateDistribution<double>

<SerializableAttribute>
Public Class Mixture(Of T As {Object, IUnivariateDistribution(Of Double)})
	Inherits UnivariateContinuousDistribution
	Implements IMixture(Of T), IDistribution, ICloneable, 
	IFittableDistribution(Of Double, MixtureOptions), IFittable(Of Double, MixtureOptions), 
	IFittable(Of Double), IFittableDistribution(Of Double), IDistribution(Of Double), 
	ISampleableDistribution(Of Double), IRandomNumberGenerator(Of Double)

// Create a new mixture containing two Normal distributions
Mixture<NormalDistribution> mix = new Mixture<NormalDistribution>(
    new NormalDistribution(2, 1), new NormalDistribution(5, 1));

// Common measures
double mean   = mix.Mean;     // 3.5
double median = mix.Median;   // 3.4999998506015895
double var    = mix.Variance; // 3.25

// Cumulative distribution functions
double cdf = mix.DistributionFunction(x: 4.2);               // 0.59897597553494908
double ccdf = mix.ComplementaryDistributionFunction(x: 4.2); // 0.40102402446505092

// Probability mass functions
double pmf1 = mix.ProbabilityDensityFunction(x: 1.2); // 0.14499174984363708
double pmf2 = mix.ProbabilityDensityFunction(x: 2.3); // 0.19590437513747333
double pmf3 = mix.ProbabilityDensityFunction(x: 3.7); // 0.13270883471234715
double lpmf = mix.LogProbabilityDensityFunction(x: 4.2); // -1.8165661905848629

// Quantile function
double icdf1 = mix.InverseDistributionFunction(p: 0.17); // 1.5866611690305095
double icdf2 = mix.InverseDistributionFunction(p: 0.46); // 3.1968506765456883
double icdf3 = mix.InverseDistributionFunction(p: 0.87); // 5.6437596300843076

// Hazard (failure rate) functions
double hf = mix.HazardFunction(x: 4.2);            // 0.40541978256972522
double chf = mix.CumulativeHazardFunction(x: 4.2); // 0.91373394208601633

// String representation:
// Mixture(x; 0.5 * N(x; μ = 5, σ² = 1) + 0.5 * N(x; μ = 5, σ² = 1))
string str = mix.ToString(CultureInfo.InvariantCulture);

// Randomly initialize some mixture components
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);

// Create an initial mixture
var mixture = new Mixture<NormalDistribution>(components);

// Now, suppose we have a weighted data
// set. Those will be the input points:

double[] points = { 0, 3, 1, 7, 3, 5, 1, 2, -1, 2, 7, 6, 8, 6 }; // (14 points)

// And those are their respective unnormalized weights:
double[] weights = { 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 3, 1, 1 }; // (14 weights)

// Let's normalize the weights so they sum up to one:
weights = weights.Divide(weights.Sum());

// Now we can fit our model to the data:
mixture.Fit(points, weights);   // done!

// Our model will be:
double mean1 = mixture.Components[0].Mean; // 1.41126
double mean2 = mixture.Components[1].Mean; // 6.53301

// With mixture weights
double pi1 = mixture.Coefficients[0]; // 0.51408
double pi2 = mixture.Coefficients[0]; // 0.48591

// If we need the GaussianMixtureModel functionality, we can
// use the estimated mixture to initialize a new model:
GaussianMixtureModel gmm = new GaussianMixtureModel(mixture);

mean1 = gmm.Gaussians[0].Mean[0]; // 1.41126 (same)
mean2 = gmm.Gaussians[1].Mean[0]; // 6.53301 (same)

p1 = gmm.Gaussians[0].Proportion; // 0.51408 (same)
p2 = gmm.Gaussians[1].Proportion; // 0.48591 (same)