ghyp (version 1.3.0)

ghyp-constructors: Create generalized hyperbolic distribution objects

Description

Constructor functions for univariate and multivariate generalized hyperbolic distribution objects and their special cases in one of the parametrizations chi/psi, alpha.bar and alpha/delta.

Usage

ghyp(lambda = 0.5, chi = 0.5, psi = 2, mu = 0, sigma = diag(rep(1, length(mu))), 
     gamma = rep(0, length(mu)), alpha.bar = NULL, data = NULL)
     
ghyp.ad(lambda = 0.5, alpha = 1.5, delta = 1, beta = rep(0, length(mu)), 
        mu = 0, Delta = diag(rep(1, length(mu))), data = NULL)     

hyp(chi = 0.5, psi = 2, mu = 0, sigma = diag(rep(1, length(mu))), 
    gamma = rep(0, length(mu)), alpha.bar = NULL, data = NULL) 
hyp.ad(alpha = 1.5, delta = 1, beta = rep(0, length(mu)), mu = 0, 
       Delta = diag(rep(1, length(mu))), data = NULL)    

NIG(chi = 2, psi = 2, mu = 0, sigma = diag(rep(1, length(mu))), 
    gamma = rep(0, length(mu)), alpha.bar = NULL, data = NULL) 
NIG.ad(alpha = 1.5, delta = 1, beta = rep(0, length(mu)), mu = 0, 
       Delta = diag(rep(1, length(mu))), data = NULL)

student.t(nu = 3.5, mu = 0, sigma = diag(rep(1, length(mu))), 
          gamma = rep(0, length(mu)), data = NULL)  
student.t.ad(lambda = -2, delta = 1, beta = rep(0, length(mu)), mu = 0, 
             Delta = diag(rep(1, length(mu))), data = NULL)

VG(lambda = 1, psi = 2*lambda, mu = 0, sigma = diag(rep(1, length(mu))), 
   gamma = rep(0, length(mu)), data = NULL)
VG.ad(lambda = 2, alpha = 1.5, beta = rep(0, length(mu)), mu = 0, 
      Delta = diag(rep(1, length(mu))), data = NULL)
gauss(mu = 0, sigma = diag(rep(1, length(mu))), data = NULL)

Arguments

lambda

Shape parameter. Common for all parametrizations.

nu

Shape parameter only used in case of a Student-t distribution in the chi/psi and alpha.bar parametrization . It determines the degree of freedom.

chi

Shape parameter of the chi/psi parametrization.

psi

Shape parameter of the chi/psi parametrization.

alpha

Shape parameter of the alpha/delta parametrization.

delta

Shape parameter of the alpha/delta parametrization.

alpha.bar

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

mu

Location parameter. Either a scalar or a vector. Common for all parametrizations.

sigma

Dispersion parameter of the chi/psi parametrization. Either a scalar or a matrix.

Delta

Dispersion parameter. Must be a matrix with a determinant of 1. This parameter is only used in the multivariate case of the alpha.beta parametrization.

gamma

Skewness parameter of the chi/psi parametrization. Either a scalar or a vector.

beta

Skewness parameter of the alpha/delta parametrization. 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

These functions serve as constructors 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. Whenever alpha.bar is not NULL it is assumed that the alpha.bar parametrization is used and the parameters chi and psi become redundant. ghyp.ad, hyp.ad, NIG.ad, student.t.ad and VG.ad use the alpha/delta parametrization. Have a look on the vignette of this package in the doc folder for further information regarding the parametrization and for the domains of variation of the parameters.

References

ghyp-package vignette in the doc folder or on http://cran.r-project.org/web/packages/ghyp/

See Also

ghyp-class for a summary of generic methods assigned to ghyp objects, coef for switching between different parametrizations, d/p/q/r/ES/gyhp for density, distribution function et cetera, fit.ghypuv and fit.ghypmv for fitting routines.

Examples

## alpha.bar parametrization of a univariate generalized hyperbolic distribution
  ghyp(lambda=2, alpha.bar=0.1, mu=0, sigma=1, gamma=0)
  ## lambda/chi parametrization of a univariate generalized hyperbolic distribution
  ghyp(lambda=2, chi=1, psi=0.5, mu=0, sigma=1, gamma=0)
  ## alpha/delta parametrization of a univariate generalized hyperbolic distribution
  ghyp.ad(lambda=2, alpha=0.5, delta=1, mu=0, beta=0)
  
  ## alpha.bar parametrization of a multivariate generalized hyperbolic distribution
  ghyp(lambda=1, alpha.bar=0.1, mu=2:3, sigma=diag(1:2), gamma=0:1)
  ## lambda/chi parametrization of a multivariate generalized hyperbolic distribution
  ghyp(lambda=1, chi=1, psi=0.5, mu=2:3, sigma=diag(1:2), gamma=0:1)
  ## alpha/delta parametrization of a multivariate generalized hyperbolic distribution
  ghyp.ad(lambda=1, alpha=2.5, delta=1, mu=2:3, Delta=diag(c(1,1)), beta=0:1)

  ## 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/delta parametrization of a univariate hyperbolic distribution
  hyp.ad(alpha=0.5, delta=1, mu=0, beta=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/delta parametrization of a univariate normal inverse gaussian distribution
  NIG.ad(alpha=0.5, delta=1, mu=0, beta=0)
  
  ## alpha.bar parametrization of a univariate variance gamma distribution   
  VG(lambda=2, mu=1, sigma=0.1, gamma=0)
  ## alpha/delta parametrization of a univariate variance gamma distribution   
  VG.ad(lambda=2, alpha=0.5, mu=0, beta=0)
  
  ## alpha.bar parametrization of a univariate Student-t distribution 
  student.t(nu = 3, mu=1, sigma=0.1, gamma=0)
  ## alpha/delta parametrization of a univariate Student-t distribution   
  student.t.ad(lambda=-2, delta=1, mu=0, beta=1)

  ## Obtain equal results as in the R-core parametrization of the Student-t distribution   
  nu <- 2.1
  t.obj <- student.t(nu = nu, sigma = sqrt(nu / (nu - 2)))
  dat <- 0.1 * 1:9
  dt(dat, nu) 
  dghyp(dat, t.obj)  
  pt(dat, nu) 
  pghyp(dat, t.obj)