MomCumGenHyp: Moments and cumulants of the multivariate Generalized...

In MultiStatM: Multivariate Statistical Methods

Moments and cumulants of the multivariate Generalized Hyperbolic distribution

Description

Computes cumulants and moments up to order r=6 of the d-variate Generalized Hyperbolic distribution \mathcal{GH}\left( \lambda ,\chi ,\psi ,\boldsymbol{\mu },\boldsymbol{\Sigma },\boldsymbol{\gamma }% \right) defined as

\mathbf{X}=\boldsymbol{\mu }+V\boldsymbol{\gamma }+\sqrt{V}\boldsymbol{% \Sigma }^{1/2}\mathbf{Z}

where \mathbf{Z}\in \mathcal{N}\left( 0,\mathbf{I}_{d}\right), V \geq 0, is independent of \mathbf{Z}, is a non-negative, scalar-valued variate, which is Generalized Inverse Gaussian (scalar valued GIG), V\in GIG\left( \lambda ,\chi ,\psi \right).

Usage

MomCumGenHyp(r = 4, lambda, chi, psi, mu, sigma, gamma, nMu = FALSE)

Arguments

r	highest order of moments and cumulants
lambda	scalar valued
chi	scalar valued
psi	scalar valued
mu	a vector of dimension d
sigma	a dxd covariance matrix
gamma	a scalar value
nMu	if it is TRUE then moments are calculated

Value

The list of moments (or cumulants) in vector form

See Also

Other Moments and cumulants: Cum2Mom(), EVSKGenHyp(), EVSKSkewNorm(), EVSKSkewt(), EVSKUniS(), Mom2Cum(), MomCumCFUSN(), MomCumMVt(), MomCumSkewNorm(), MomCumUniS(), MomCumZabs()

Examples

lambda <- 1
chi <- 2
psi <- 2
mu <- rep(0,2)
sigma <- diag(2)
gamma <-  c(0.2,0.5)
MomCumGenHyp(r=4,lambda, chi, psi, mu, sigma, gamma)

MultiStatM documentation built on Jan. 25, 2026, 5:06 p.m.