mnormalgamma {lestat}

A Multivariate Normal-Gamma Distribution

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 \mu, P, \alpha, and \beta, then the marginal distribution of y has a Gamma distribution with parameters \alpha, \beta, and conditionally on y, x has a multivariate normal distribution with expectation \mu and precision matrix yP. The probability density is proportional to

f(x,y)=y^{\alpha+k/2-1}\exp(-y(\beta + (x-\mu)^tP(x-\mu)/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))