|
DirichletDistribution Class |
Dirichlet distribution.
Inheritance HierarchySystemObject
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.MultivariateMultivariateContinuousDistribution
Accord.Statistics.Distributions.MultivariateDirichletDistribution
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.MultivariateMultivariateContinuousDistribution
Accord.Statistics.Distributions.MultivariateDirichletDistribution
Namespace: Accord.Statistics.Distributions.Multivariate
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0
Syntax[SerializableAttribute] public class DirichletDistribution : MultivariateContinuousDistribution
The DirichletDistribution type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | DirichletDistribution(Double) |
Creates a new Dirichlet distribution.
|
| DirichletDistribution(Int32, Double) |
Creates a new symmetric Dirichlet distribution.
|
Properties| Name | Description | |
|---|---|---|
 | Covariance |
Gets the variance-covariance 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 for this distribution.
(Overrides MultivariateContinuousDistributionVariance.) |
Methods| 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 |
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from MultivariateContinuousDistribution.) |
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
 | 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, Double, IFittingOptions) |
Not supported.
(Overrides MultivariateContinuousDistributionFit(Double, Double, IFittingOptions).) |
| Fit(Double, Int32, IFittingOptions) |
Fits the underlying distribution to a given set of observations.
(Inherited from MultivariateContinuousDistribution.) |
| 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, Double, Random) |
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.) |
| Generate(Int32, Int32, Random) |
Generates a random vector of observations from the current distribution.
(Inherited from MultivariateContinuousDistribution.) |
| 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 |
Not supported.
(Overrides MultivariateContinuousDistributionInnerDistributionFunction(Double).) |
| InnerLogProbabilityDensityFunction |
Gets the log-probability 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).) |
| LogProbabilityDensityFunction |
Gets the log-probability density function (pdf)
for this distribution evaluated at point x.
(Inherited from MultivariateContinuousDistribution.) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| ProbabilityDensityFunction |
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from MultivariateContinuousDistribution.) |
| 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).) |
Extension Methods| 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.) |
RemarksThe Dirichlet distribution, often denoted Dir(α), is a family of continuous multivariate probability distributions parameterized by a vector α of positive real numbers. It is the multivariate generalization of the beta distribution.
Dirichlet distributions are very often used as prior distributions in Bayesian statistics, and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution. That is, its probability density function returns the belief that the probabilities of K rival events are xi given that each event has been observed αi−1 times.
References:
Examples// Create a Dirichlet with the following concentrations var dirich = new DirichletDistribution(0.42, 0.57, 1.2); // Common measures double[] mean = dirich.Mean; // { 0.19, 0.26, 0.54 } double[] median = dirich.Median; // { 0.19, 0.26, 0.54 } double[] var = dirich.Variance; // { 0.048, 0.060, 0.077 } double[,] cov = dirich.Covariance; // see below // 0.0115297440926238 0.0156475098399895 0.0329421259789253 // cov = 0.0156475098399895 0.0212359062114143 0.0447071709713986 // 0.0329421259789253 0.0447071709713986 0.0941203599397865 // (the above matrix representation has been transcribed to text using) string str = cov.ToString(DefaultMatrixFormatProvider.InvariantCulture); // Probability mass functions double pdf1 = dirich.ProbabilityDensityFunction(new double[] { 2, 5 }); // 0.12121671541846207 double pdf2 = dirich.ProbabilityDensityFunction(new double[] { 4, 2 }); // 0.12024840322466089 double pdf3 = dirich.ProbabilityDensityFunction(new double[] { 3, 7 }); // 0.082907634905068528 double lpdf = dirich.LogProbabilityDensityFunction(new double[] { 3, 7 }); // -2.4900281233124044
See Also