QRM (version 0.4-7)

GIG: Generalized Inverse Gaussian Distribution

Description

Calculates (log) moments of univariate generalized inverse Gaussian (GIG) distribution and generating random variates.

Usage

EGIG(lambda, chi, psi, k = 1)
ElogGIG(lambda, chi, psi)
rGIG(n, lambda, chi, psi, envplot = FALSE, messages = FALSE)

Arguments

chi

numeric, chi parameter.

envplot

logical, whether plot of rejection envelope should be created.

k

integer, order of moments.

lambda

numeric, lambda parameter.

messages

logical, whether a message about rejection rate should be returned.

n

integer, count of random variates.

psi

numeric, psi parameter.

Value

• (log) mean of distribution or vector random variates in case of rgig().

Details

Normal variance mixtures are frequently obtained by perturbing the variance component of a normal distribution; here this is done by multiplying the square root of a mixing variable assumed to have a GIG distribution depending upon three parameters $(\lambda, \chi, \psi)$. See p.77 in QRM. Normal mean-variance mixtures are created from normal variance mixtures by applying another perturbation of the same mixing variable to the mean component of a normal distribution. These perturbations create Generalized Hyperbolic Distributions. See pp. 78--81 in QRM. A description of the GIG is given on page 497 in QRM Book.