mnormalexpgamma {lestat}

A Multivariate Normal-ExpGamma Distribution

Description

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

Usage

mnormalexpgamma(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-ExpGamma distribution with parameters \mu, P, \alpha, and \beta, then the marginal distribution of y has an ExpGamma distribution with parameters \alpha, \beta, and -2, and conditionally on y, x has a multivariate normal distribution with expectation \mu and precision matrix e^{-2y}P. The probability density is proportional to

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

where k is the dimension.

Value

A multivariate Normal-ExpGamma probability distribution.

Author(s)

Petter Mostad <[e-mail]>

See Also

gamma,normal,expgamma, normalgamma,normalexpgamma mnormal,mnormalgamma

Examples

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