lestat (version 1.9)

normalexpgamma: A Normal-ExpGamma Distribution

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

normalexpgamma(mu, kappa, alpha, beta)

Arguments

mu

The mu parameter.

kappa

The kappa parameter.

alpha

The alpha parameter.

beta

The beta parameter.

Value

A Normal-ExpGamma probability distribution.

Details

If $(x,y)$ has a Normal-ExpGamma distribution with parameters $\mu$, $\kappa$, $\alpha$, 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 normal distribution with expectation $\mu$ and logged standard deviation $\kappa +y$. The probability density is proportional to $$f(x,y)=\exp (-(2\alpha +1)y-e^{-2y}(\beta +e^{-2\kappa }(x-\mu {)}^2/2))$$

See Also

gamma, normal, expgamma, normalgamma, mnormal, mnormalgamma, mnormalexpgamma

Examples

# NOT RUN {
plot(normalexpgamma(3,4,5,6))
# }