EVSKGenHyp: EVSK multivariate Generalized hyperbolic

In MultiStatM: Multivariate Statistical Methods

EVSK multivariate Generalized hyperbolic

Description

Computes the theoretical values of the mean, variance, skewness and (excess) kurtosis vectors for 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

EVSKGenHyp(lambda, chi, psi, mu, sigma, gamma)

Arguments

lambda	scalar valued
chi	scalar valued
psi	scalar valued
mu	a vector of dimension d
sigma	a dxd covariance matrix
gamma	a scalar value

Value

A list of theoretical values for the mean, variance, skewness and kurtosis vectors

References

A.J. McNeil, R. Frey, and P. Embrechts. Quantitative risk management: concepts, techniques and tools-revised edition. Princeton university press, 2015.

See Also

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

Examples

lambda <- 1
chi <- 2
psi <- 2
mu <- rep(0,2)
sigma <- diag(2)
gamma <-  c(0.2,0.5)
EVSKGenHyp(lambda, chi, psi, mu, sigma, gamma)

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