normalgamma {lestat}

A Normal-Gamma Distribution

Description

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

Usage

normalgamma(mu, kappa, alpha, beta)

Arguments

mu

The mu parameter.

kappa

The kappa parameter.

alpha

The alpha parameter.

beta

The beta parameter.

Details

If (x,y) has a Normal-Gamma distribution with parameters \mu, \kappa, \alpha, and \beta, then the marginal distribution of y has a Gamma distribution with parameters \alpha and \beta, and conditionally on y, x has a normal distribution with expectation \mu and logged standard deviation \kappa - log(y)/2. The probability density is proportional to

f(x,y)=y^{\alpha-0.5}\exp(-y(\beta + e^{-2\kappa}(x-\mu)^2/2))

Value

A Normal-Gamma probability distribution.

Author(s)

Petter Mostad <[e-mail]>

See Also

gamma, normal, expgamma, normalexpgamma, mnormal, mnormalgamma, mnormalexpgamma

Examples

plot(normalgamma(3,4,5,6))