Calculates (log) moments of univariate generalized inverse Gaussian (GIG) distribution and generating random variates.
EGIG(lambda, chi, psi, k = 1)
ElogGIG(lambda, chi, psi)
rGIG(n, lambda, chi, psi, envplot = FALSE, messages = FALSE)(log) mean of distribution or vector random variates in case of
rgig().
numeric, chi parameter.
logical, whether plot of rejection envelope
should be created.
integer, order of moments.
numeric, lambda parameter.
logical, whether a message about rejection rate
should be returned.
integer, count of random variates.
numeric, psi parameter.
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.