ghyp (version 1.1.0)

ghyp-constructors: Create generalized hyperbolic distribution objects

Description

Constructor function for univariate and multivariate generalized hyperbolic objects and its special cases.

Usage

ghyp(lambda = 0.5, chi = 0.5, psi = 2, mu = 0, sigma = 1, gamma = 0, 
     alpha.bar = NULL, data = NULL)
hyp(chi = 0.5, psi = 2, mu = 0, sigma = 1, gamma = 0, alpha.bar = NULL, 
    data = NULL) 
NIG(chi = 2, psi = 2, mu = 0, sigma = 1, gamma = 0, alpha.bar = NULL, 
    data = NULL) 
student.t(nu = 3.5, mu = 0, sigma = 1, gamma = 0, data = NULL)  
VG(lambda = 1, psi = 2*lambda, mu = 0, sigma = 1, gamma = 0, data = NULL)

Arguments

lambda

Shape parameter.

nu

Shape parameter only used in case of a student-t distribution. It determines the degree of freedom.

chi

Shape parameter of the alternative chi/psi parametrization.

psi

Shape parameter of the alternative chi/psi parametrization.

alpha.bar

Shape parameter of the alternative alpha.bar parametrization. Supplying alpha.bar makes the parameters chi and psi redundant.

mu

Location parameter. Either a scalar or a vector.

sigma

Dispersion parameter. Either a scalar or a matrix.

gamma

Skewness parameter. Either a scalar or a vector.

data

An object coercible to a vector (univariate case) or matrix (multivariate case).

Value

• An object of class ghyp.

Details

This function serves as a constructor for univariate and multivariate generalized hyperbolic distribution objects and the special cases of the generalized hyperbolic distribution. ghyp, hyp and NIG can be called either with the chi/psi or the alpha.bar parametrization. When ever alpha.bar is not NULL it is assumed that the alpha.bar parametrization is used and the parameters chi and psi become redundant.

See Also

ghyp-class for a summary of generic methods belonging to ghyp objects, fit.ghypuv and fit.ghypmv for fitting routines.

Examples

## alpha.bar parametrization of a univariate generalized hyperbolic distribution
  ghyp(lambda=1, alpha.bar=0.1, mu=0, sigma=1, gamma=0)
  ## lambda/chi parametrization of a univariate generalized hyperbolic distribution
  ghyp(lambda=1, chi=1, psi=0.5, mu=0, sigma=1, gamma=0)
  
  ## alpha.bar parametrization of a multivariate generalized hyperbolic distribution
  ghyp(lambda=1, alpha.bar=0.1, mu=rep(0,2), sigma=diag(rep(1,2)), gamma=rep(0,2))
  ## lambda/chi parametrization of a multivariate generalized hyperbolic distribution
  ghyp(lambda=1, chi=1, psi=0.5, mu=rep(0,2), sigma=diag(rep(1,2)), gamma=rep(0,2))

  ## alpha.bar parametrization of a univariate hyperbolic distribution
  hyp(alpha.bar=0.3, mu=1, sigma=0.1, gamma=0)
  ## lambda/chi parametrization of a univariate hyperbolic distribution
  hyp(chi=1, psi=2, mu=1, sigma=0.1, gamma=0)

  ## alpha.bar parametrization of a univariate normal inverse gaussian distribution
  NIG(alpha.bar=0.3, mu=1, sigma=0.1, gamma=0)
  ## lambda/chi parametrization of a univariate normal inverse gaussian distribution
  NIG(chi=1, psi=2, mu=1, sigma=0.1, gamma=0)
  
  ## alpha.bar parametrization of a univariate variance gamma distribution   
  VG(lambda=2, mu=1, sigma=0.1, gamma=0)
  
  ## alpha.bar parametrization of a univariate student-t distribution 
  student.t(nu = 3, mu=1, sigma=0.1, gamma=0)