mnormalgamma {lestat}R Documentation

A Multivariate Normal-Gamma Distribution

Description

Creates an object representing a multivariate Normal-Gamma distribution. If (x,y)(x,y) has a multivariate Normal-Gamma distribution, then the marginal distribution of yy is an Gamma distribution, and the conditional distribution of xx given yy 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)(x,y) has a multivariate Normal-Gamma distribution with parameters μ\mu, PP, α\alpha, and β\beta, then the marginal distribution of yy has a Gamma distribution with parameters α\alpha, β\beta, and conditionally on yy, xx has a multivariate normal distribution with expectation μ\mu and precision matrix yPyP. The probability density is proportional to

f(x,y)=yα+k/21exp(y(β+(xμ)tP(xμ)/2)) f(x,y)=y^{\alpha+k/2-1}\exp(-y(\beta + (x-\mu)^tP(x-\mu)/2))

where kk is the dimension.

Value

A multivariate Normal-Gamma probability distribution.

Author(s)

Petter Mostad <mostad@chalmers.se>

See Also

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

Examples

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

[Package lestat version 1.9 Index]