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Accord.NET (logo) InverseWishartDistribution Class
Inverse Wishart Distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.MultivariateMultivariateContinuousDistribution
      Accord.Statistics.Distributions.MultivariateInverseWishartDistribution

Namespace:  Accord.Statistics.Distributions.Multivariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.4.0
Syntax
[SerializableAttribute]
public class InverseWishartDistribution : MultivariateContinuousDistribution
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The InverseWishartDistribution type exposes the following members.

Constructors
  NameDescription
Public methodInverseWishartDistribution
Creates a new Inverse Wishart distribution.
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Properties
  NameDescription
Public propertyCovariance
Gets the variance-covariance matrix for this distribution.
(Overrides MultivariateContinuousDistributionCovariance.)
Public propertyDimension
Gets the number of variables for this distribution.
(Inherited from MultivariateContinuousDistribution.)
Public propertyMean
Gets the mean for this distribution as a flat matrix.
(Overrides MultivariateContinuousDistributionMean.)
Public propertyMeanMatrix
Gets the mean for this distribution.
Public propertyMedian
Gets the median for this distribution.
(Inherited from MultivariateContinuousDistribution.)
Public propertyMode
Gets the mode for this distribution.
(Inherited from MultivariateContinuousDistribution.)
Public propertyVariance
Gets the variance for this distribution.
(Overrides MultivariateContinuousDistributionVariance.)
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Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)
Public methodComplementaryDistributionFunction
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.)
Public methodDistributionFunction
Not supported.
(Overrides MultivariateContinuousDistributionDistributionFunction(Double).)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodFit(Double)
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)
Public methodFit(Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)
Public methodFit(Double, Double)
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)
Public methodFit(Double, Int32)
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)
Public methodFit(Double, Double, IFittingOptions)
Not supported.
(Overrides MultivariateContinuousDistributionFit(Double, Double, IFittingOptions).)
Public methodFit(Double, Int32, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.)
Public methodGenerate
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)
Public methodGenerate(Double)
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)
Public methodGenerate(Int32)
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.)
Public methodGenerate(Int32)
Generates a random observation from the current distribution.
(Inherited from MultivariateContinuousDistribution.)
Public methodGenerate(Int32, Double)
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.)
Public methodGenerate(Int32, Int32)
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodLogProbabilityDensityFunction(Double)
Gets the probability density function (pdf) for this distribution evaluated at point x.
Public methodLogProbabilityDensityFunction(Double)
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Overrides MultivariateContinuousDistributionLogProbabilityDensityFunction(Double).)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodProbabilityDensityFunction(Double)
Gets the probability density function (pdf) for this distribution evaluated at point x.
Public methodProbabilityDensityFunction(Double)
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Overrides MultivariateContinuousDistributionProbabilityDensityFunction(Double).)
Public methodToString
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(IFormatProvider)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String, IFormatProvider)
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodToTOverloaded.
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.)
Public Extension MethodToTOverloaded.
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 Matrix.)
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Remarks

The inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a multivariate normal distribution.

References:

Examples
// Create a Inverse Wishart with the parameters
var invWishart = new InverseWishartDistribution(

    // Degrees of freedom
    degreesOfFreedom: 4,

    // Scale parameter
    inverseScale: new double[,] 
    {
         {  1.7, -0.2 },
         { -0.2,  5.3 },
    }
);

// Common measures
double[] var = invWishart.Variance;  // { -3.4, -10.6 }
double[,] cov = invWishart.Covariance;  // see below
double[,] mmean = invWishart.MeanMatrix; // see below

//        cov                mean
//   -5.78   -4.56        1.7  -0.2 
//   -4.56  -56.18       -0.2   5.3 

// (the above matrix representations have been transcribed to text using)
string scov = cov.ToString(DefaultMatrixFormatProvider.InvariantCulture);
string smean = mmean.ToString(DefaultMatrixFormatProvider.InvariantCulture);

// For compatibility reasons, .Mean stores a flattened mean matrix
double[] mean = invWishart.Mean; // { 1.7, -0.2, -0.2, 5.3 }


// Probability density functions
double pdf = invWishart.ProbabilityDensityFunction(new double[,] 
{
    {  5.2,  0.2 }, // 0.000029806281690351203
    {  0.2,  4.2 },
});

double lpdf = invWishart.LogProbabilityDensityFunction(new double[,] 
{
    {  5.2,  0.2 }, // -10.420791391688828
    {  0.2,  4.2 },
});
See Also