# normalexpgamma: A Normal-ExpGamma Distribution In lestat: A Package for Learning Statistics

## Description

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

## Usage

 `1` ```normalexpgamma(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-ExpGamma distribution with parameters μ, κ, α, and β, then the marginal distribution of y has an ExpGamma distribution with parameters α, β, and -2, and conditionally on y, x has a normal distribution with expectation μ and logged standard deviation κ + y. The probability density is proportional to

f(x,y)=\exp(-(2α + 1)y - e^{-2y}(β + e^{-2κ}(x-μ)^2/2))

## Value

A Normal-ExpGamma probability distribution.

## Author(s)

`gamma`, `normal`, `expgamma`, `normalgamma`, `mnormal`, `mnormalgamma`, `mnormalexpgamma`
 `1` ```plot(normalexpgamma(3,4,5,6)) ```