# 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

 `1` ```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 <mostad@chalmers.se>

## See Also

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

## Examples

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

### Example output

```Loading required package: MASS
```

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