MultivariateMixtureT Class 
Namespace: Accord.Statistics.Distributions.Multivariate
[SerializableAttribute] public class MultivariateMixture<T> : MultivariateContinuousDistribution, IMixture<T>, IDistribution, ICloneable, IFittableDistribution<double[], MixtureOptions>, IFittable<double[], MixtureOptions>, IFittable<double[]>, IFittableDistribution<double[]>, IDistribution<double[]>, ISampleableDistribution<double[]>, IRandomNumberGenerator<double[]> where T : Object, IMultivariateDistribution<double[]>
The MultivariateMixtureT type exposes the following members.
Name  Description  

MultivariateMixtureT(T) 
Initializes a new instance of the MultivariateMixtureT class.
 
MultivariateMixtureT(Double, T) 
Initializes a new instance of the MultivariateMixtureT class.

Name  Description  

Coefficients 
Gets the weight coefficients.
 
Components 
Gets the mixture components.
 
Covariance 
Gets the variancecovariance matrix for this distribution.
(Overrides MultivariateContinuousDistributionCovariance.)  
Dimension 
Gets the number of variables for this distribution.
(Inherited from MultivariateContinuousDistribution.)  
Mean 
Gets the mean for this distribution.
(Overrides MultivariateContinuousDistributionMean.)  
Median 
Gets the median for this distribution.
(Inherited from MultivariateContinuousDistribution.)  
Mode 
Gets the mode for this distribution.
(Inherited from MultivariateContinuousDistribution.)  
Variance 
Gets the variance vector for this distribution.
(Overrides MultivariateContinuousDistributionVariance.) 
Name  Description  

Clone 
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)  
ComplementaryDistributionFunction 
Gets the complementary cumulative distribution function
(ccdf) for this distribution evaluated at point x.
This function is also known as the Survival function.
(Inherited from MultivariateContinuousDistribution.)  
DistributionFunction(Double) 
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from MultivariateContinuousDistribution.)  
DistributionFunction(Int32, Double) 
Gets the cumulative distribution function (cdf) for one
of the component distributions evaluated at point x.
 
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Estimate(Double, T) 
Estimates a new mixture model from a given set of observations.
 
Estimate(Double, Double, T) 
Estimates a new mixture model from a given set of observations.
 
Estimate(Double, Double, Double, T) 
Estimates a new mixture model from a given set of observations.
 
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
Fit(Double) 
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)  
Fit(Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)  
Fit(Double, Double) 
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)  
Fit(Double, Int32) 
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)  
Fit(Double, Int32, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)  
Fit(Double, Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Overrides MultivariateContinuousDistributionFit(Double, Double, IFittingOptions).)  
Fit(Double, Double, MixtureOptions) 
Fits the underlying distribution to a given set of observations.
 
Generate 
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Double) 
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Int32) 
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Int32) 
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Random) 
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Double, Random) 
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Int32, Double) 
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Int32, Int32) 
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Int32, Random) 
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Int32, Random) 
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Int32, Int32, Random) 
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.)  
Generate(Int32, Double, Random) 
Generates a random vector of observations from the current distribution.
(Overrides MultivariateContinuousDistributionGenerate(Int32, Double, Random).)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
InnerComplementaryDistributionFunction 
Gets the complementary cumulative distribution function
(ccdf) for this distribution evaluated at point x.
This function is also known as the Survival function.
(Inherited from MultivariateContinuousDistribution.)  
InnerDistributionFunction 
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point x.
(Overrides MultivariateContinuousDistributionInnerDistributionFunction(Double).)  
InnerLogProbabilityDensityFunction 
Gets the logprobability density function (pdf) for
this distribution evaluated at point x.
(Overrides MultivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)  
InnerProbabilityDensityFunction 
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Overrides MultivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)  
LogLikelihood(Double) 
Computes the loglikelihood of the distribution
for a given set of observations.
 
LogLikelihood(Double, Double) 
Computes the loglikelihood of the distribution
for a given set of observations.
 
LogProbabilityDensityFunction(Double) 
Gets the logprobability density function (pdf)
for this distribution evaluated at point x.
(Inherited from MultivariateContinuousDistribution.)  
LogProbabilityDensityFunction(Int32, Double) 
Gets the logprobability density function (pdf) for one
of the component distributions evaluated at point x.
 
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
ProbabilityDensityFunction(Double) 
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from MultivariateContinuousDistribution.)  
ProbabilityDensityFunction(Int32, Double) 
Gets the probability density function (pdf) for one of
the component distributions evaluated at point x.
 
ToString 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(IFormatProvider) 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(String) 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(String, IFormatProvider) 
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).) 
Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)  
IsEqual 
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.)  
To(Type)  Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)  
ToT  Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) 
A mixture density is a probability density function which is expressed as a convex combination (i.e. a weighted sum, with nonnegative weights that sum to 1) of other probability density functions. The individual density functions that are combined to make the mixture density are called the mixture components, and the weights associated with each component are called the mixture weights.
References:
// Randomly initialize some mixture components MultivariateNormalDistribution[] components = new MultivariateNormalDistribution[2]; components[0] = new MultivariateNormalDistribution(new double[] { 2 }, new double[,] { { 1 } }); components[1] = new MultivariateNormalDistribution(new double[] { 5 }, new double[,] { { 1 } }); // Create an initial mixture var mixture = new MultivariateMixture<MultivariateNormalDistribution>(components); // Now, suppose we have a weighted data // set. Those will be the input points: double[][] points = new double[] { 0, 3, 1, 7, 3, 5, 1, 2, 1, 2, 7, 6, 8, 6 } // (14 points) .ToArray(); // 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[0]; // 1.41126 double mean2 = mixture.Components[1].Mean[0]; // 6.53301 // With mixture coefficients double pi1 = mixture.Coefficients[0]; // 0.51408489193241225 double pi2 = mixture.Coefficients[1]; // 0.48591510806758775 // 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)