dist.Inverse.Matrix.Gamma: Inverse Matrix Gamma Distribution

Description Usage Arguments Details Value Author(s) See Also Examples

Description

This function provides the density for the inverse matrix gamma distribution.

Usage

1
dinvmatrixgamma(X, alpha, beta, Psi, log=FALSE)

Arguments

X

This is a k x k positive-definite covariance matrix.

alpha

This is a scalar shape parameter (the degrees of freedom), alpha.

beta

This is a scalar, positive-only scale parameter, beta.

Psi

This is a k x k positive-definite scale matrix.

log

Logical. If log=TRUE, then the logarithm of the density is returned.

Details

The inverse matrix gamma (IMG), also called the inverse matrix-variate gamma, distribution is a generalization of the inverse gamma distribution to positive-definite matrices. It is a more general and flexible version of the inverse Wishart distribution (dinvwishart), and is a conjugate prior of the covariance matrix of a multivariate normal distribution (dmvn) and matrix normal distribution (dmatrixnorm).

The compound distribution resulting from compounding a matrix normal with an inverse matrix gamma prior over the covariance matrix is a generalized matrix t-distribution.

The inverse matrix gamma distribution is identical to the inverse Wishart distribution when alpha = nu / 2 and beta = 2.

Value

dinvmatrixgamma gives the density.

Author(s)

Statisticat, LLC. [email protected]

See Also

dinvgamma dmatrixnorm, dmvn, and dinvwishart

Examples

1
2
3
4
library(LaplacesDemon)
k <- 10
dinvmatrixgamma(X=diag(k), alpha=(k+1)/2, beta=2, Psi=diag(k), log=TRUE)
dinvwishart(Sigma=diag(k), nu=k+1, S=diag(k), log=TRUE)

LaplacesDemonR/LaplacesDemon documentation built on Dec. 19, 2017, 6:08 p.m.