mnormalgamma: A Multivariate Normal-Gamma Distribution

In lestat: A Package for Learning Statistics

Description

Creates an object representing a multivariate Normal-Gamma distribution. If (x,y) has a multivariate Normal-Gamma distribution, then the marginal distribution of y is an Gamma distribution, and the conditional distribution of x given y is multivariate normal.

Usage

mnormalgamma(mu=c(0,0), P, alpha, beta)

Arguments

mu	The mu parameter. It must be a vector of length at least 2. The default value is (0,0).
P	The P parameter.
alpha	The alpha parameter.
beta	The beta parameter.

Details

If (x,y) has a multivariate Normal-Gamma distribution with parameters μ, P, α, and β, then the marginal distribution of y has a Gamma distribution with parameters α, β, and conditionally on y, x has a multivariate normal distribution with expectation μ and precision matrix yP. The probability density is proportional to

f(x,y)=y^{α+k/2-1}\exp(-y(β + (x-μ)^tP(x-μ)/2))

where k is the dimension.

Value

A multivariate Normal-Gamma probability distribution.

Author(s)

Petter Mostad <[e-mail]>

See Also

gamma,normal,expgamma, normalgamma, normalexpgamma, mnormal,mnormalexpgamma

Examples

plot(mnormalgamma(alpha=3, beta=3))

Example output

Loading required package: MASS

lestat documentation built on May 2, 2019, 2:09 p.m.