MultiStatM (version 2.1.0)

EVSKGenHyp: 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)

Value

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

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

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)