ghyp-constructors            package:ghyp            R Documentation

_C_r_e_a_t_e _g_e_n_e_r_a_l_i_z_e_d _h_y_p_e_r_b_o_l_i_c _d_i_s_t_r_i_b_u_t_i_o_n _o_b_j_e_c_t_s

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

     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)

_A_r_g_u_m_e_n_t_s:

  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).

_D_e_t_a_i_l_s:

     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.

_V_a_l_u_e:

     An object of class 'ghyp'.

_N_o_t_e:

     The Student-t parametrization obtained via the "alpha.bar"
     parametrization slightly differs from the common student-t
     parametrization: The parameter 'sigma' denotes the standard
     deviation in the univariate case and the variance in the
     multivariate 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.  Have a look on the
     vignette of this package in the 'doc' folder. 

     Once an object of class 'ghyp' 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()'.

_A_u_t_h_o_r(_s):

     David Lthi

_S_e_e _A_l_s_o:

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

_E_x_a_m_p_l_e_s:

       ## 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)

