ghyp {ghyp}R Documentation

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 = 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 and is defined as -2*lambda.
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.
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 Can be of type vector, matrix or data.frame.

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 can be called either with the “chi/psi” or the “alpha.bar” parametrization. When ever alpha.bar is not NULL it is assumed that “alpha.bar” parameters were supplied.
The parametrization of the student.t distribution slightly differs from the common student-t parametrization: The parameter sigma denotes the standard deviation.
Have a look on the vignette of this package in the doc folder.

Value

An object of class ghypuv or ghypmv.

Note

The “alpha.bar” parametrization yields to a slightly different student-t parametrization: The parameter sigma denotes the variance in the multivariate case and the standard deviation in the univariate case. Thus, set sigma = sqrt(nu /(nu-2) in the univariate case to get the same results as with the standard R implementation of the student-t distribution.

Once an object of class ghypuv or ghypmv is created the methods Xghyp have to be used even when the distribution is a special case of the generalized hyperbolic distribution. E.g. do not use dVG. Use dghyp and submit a variance gamma distribution created with VG.

Author(s)

David Lüthi

See Also

ghypuv-class, ghypmv-class, fit.ghypuv, fit.ghypmv.

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)

[Package ghyp version 0.9.3 Index]