normalexpgamma {lestat}R Documentation

A Normal-ExpGamma Distribution

Description

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

Details

If (x,y)(x,y) has a Normal-ExpGamma distribution with parameters μ\mu, κ\kappa, α\alpha, and β\beta, then the marginal distribution of yy has an ExpGamma distribution with parameters α\alpha, β\beta, and -2, and conditionally on yy, xx has a normal distribution with expectation μ\mu and logged standard deviation κ+y\kappa + y. The probability density is proportional to

f(x,y)=exp((2α+1)ye2y(β+e2κ(xμ)2/2)) f(x,y)=\exp(-(2\alpha + 1)y - e^{-2y}(\beta + e^{-2\kappa}(x-\mu)^2/2))

Value

A Normal-ExpGamma probability distribution.

Author(s)

Petter Mostad <mostad@chalmers.se>

See Also

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

Examples

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

[Package lestat version 1.9 Index]