Wishart

The Wishart distribution is a generalization to multiple dimensions of the chi-square distribution, or, in the case of non-integer degrees of freedom, of the gamma distribution.

It is any of a family of probability distributions defined over symmetric, nonnegative-definite matrix-valued random variables ("random matrices"). These distributions are of great importance in the estimation of covariance matrices in multivariate statistics.

Wishart distribution parameters are scale matrix V and number of degrees of freedom n.

This topic contains the following sections:

Constructors
Methods
Properties

Constructors

Constructor	Description	Performance
set scale matrix V and degrees of freedom n	Creates new instance of Wishart with user specified parameters. Wishart(Matrix, Double)
set V, n and random generator	Creates new instance of Wishart with user specified parameters. Wishart(RandomGenerator, Matrix, Double)

Constructor

Description

Performance

set scale matrix V and degrees of freedom n

Creates new instance of Wishart with user specified parameters.

method Wishart(Matrix, Double)

set V, n and random generator

Creates new instance of Wishart with user specified parameters.

method Wishart(RandomGenerator, Matrix, Double)

Methods

Method	Description	Performance
sample	Generate random variable sample. In place: Sample(Matrix) Returning result: Sample(Matrix, Double) Sample(RandomGenerator, Matrix, Double)
pdf	Probability density function. where p is the order of the matrix V, and Γ is the multivariate gamma function. Pdf(Matrix) Pdf(Matrix, Matrix, Double)

Method

Description

Performance

sample

Generate random variable sample.

In place:

method Sample(Matrix)

Returning result:

Static Sample(Matrix, Double)

Static Sample(RandomGenerator, Matrix, Double)

pdf

Probability density function.

where p is the order of the matrix V, and Γ is the multivariate gamma function.

method Pdf(Matrix)

Static Pdf(Matrix, Matrix, Double)

Properties

Property	Description	Performance
scale	Scale matrix. Scale
degrees of freedom	Number of degrees of freedom. DegreesOfFreedom
scale is positive definite	Indicates whether user specified scale matrix is positive definite. ScaleIsPositiveDefinite
mean	Means matrix. Mean
mode	Modes matrix. Mode
generation method	Method of normal distribution generation. See Normal Method