dist.Matrix.Gamma {LaplacesDemon} | R Documentation |
Matrix Gamma Distribution
Description
This function provides the density for the matrix gamma distribution.
Usage
dmatrixgamma(X, alpha, beta, Sigma, log=FALSE)
Arguments
X |
This is a |
alpha |
This is a scalar shape parameter (the degrees of freedom),
|
beta |
This is a scalar, positive-only scale parameter,
|
Sigma |
This is a |
log |
Logical. If |
Details
Application: Continuous Multivariate Matrix
Density:
Inventors: Unknown
Notation 1:
Notation 2:
Parameter 1: shape
Parameter 2: scale
Parameter 3: positive-definite
scale matrix
Mean:
Variance:
Mode:
The matrix gamma (MG), also called the matrix-variate gamma,
distribution is a generalization of the gamma distribution to
positive-definite matrices. It is a more general and flexible version of
the Wishart distribution (dwishart
), and is a conjugate
prior of the precision matrix of a multivariate normal distribution
(dmvnp
) and matrix normal distribution
(dmatrixnorm
).
The compound distribution resulting from compounding a matrix normal with a matrix gamma prior over the precision matrix is a generalized matrix t-distribution.
The matrix gamma distribution is identical to the Wishart distribution
when and
.
Value
dmatrixgamma
gives the density.
Author(s)
Statisticat, LLC. software@bayesian-inference.com
See Also
dgamma
dmatrixnorm
,
dmvnp
, and
dwishart
Examples
library(LaplacesDemon)
k <- 10
dmatrixgamma(X=diag(k), alpha=(k+1)/2, beta=2, Sigma=diag(k), log=TRUE)
dwishart(Omega=diag(k), nu=k+1, S=diag(k), log=TRUE)