CopulaeClass            package:fCopulae            R Documentation

_B_i_v_a_r_i_a_t_e _C_o_p_u_l_a_e _C_l_a_s_s

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

     A collection and description of functions to specify the  copula
     class and to investigate bivariate Frechet copulae.  

     The class representation and methods are:

       'fCOPULA'  representation for an S4 object of class "fCOPULA",
       'show'     S4 print method.

     Frechet Copulae:

       'pfrechetCopula'  computes Frechet copula probability.

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

     show.fCOPULA(object)

     pfrechetCopula(u = 0.5, v = u, type = c("m", "pi", "w"), 
         output = c("vector", "list"))
         

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

  object: [show] - 
           an S4 object of class '"fCOPULA"'. 

  output: [*frechetCopula] - 
           output - a character string specifying how the output should
          be formatted. By default a vector of the same length as 'u' 
          and 'v'. If specified as '"list"' then 'u' and  'v' are
          expected to span a two-dimensional grid as outputted  by the
          function 'grid2d' and the function returns a list with
          elements '$x', 'y', and 'z' which can be directly  used for
          example by 2D plotting functions. 

    type: [*frechetCopula] - 
           the type of the Frechet copula. A character string selected
          from: '"m"', '"pi"', or '"w"'. 

    u, v: two numeric values or vectors of the same length at which the
          copula will be computed. If 'u' is a list then the the '$x'
          and '$y' elements will be used as 'u'  and 'v'. If 'u' is a
          two column matrix then the  first column will be used as 'u'
          and the the second  as 'v'. 

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

     The function 'pfrechetCopula' returns a numeric matrix of 
     probabilities computed at grid positions 'u'|'v'. The arguments
     'u' and 'v' are two single values or two  numeric vectors of the
     same length. If 'v' is not specified then the same values are
     taken as for 'u'. Alternatively, 'u' may be given as a two column
     vector or as a list with two entries as vectors. The first column
     or entry is taken as 'u' and the second as 'v'.

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

     The print method 'show' returns an S4 object of  class
     '"fCOPULA"'. The object contains the following slots:

   @call: the function call.   

 @copula: the name of the copula. 

  @param: a list whose elements specify the model parameters of the
          copula. 

  @title: a character string with the name of the copula. This can be 
          overwritten specifying a user defined input argument. 

@description: a character string with an optional user defined
          description.  By default just the current date will be
          returned. 


     The function 'pfrechetCopula' returns a numeric vector of 
     probabilities. An attribute named '"control"' is added which
     returns the name of the Frechet copula.

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

     Diethelm Wuertz for the Rmetrics R-port.

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

     ## fCOPULA -
        getClass("fCOPULA")
        
     ## pcopula -
        # The Frechet Copula - m:
        pfrechetCopula(0.5)
        pfrechetCopula(0.25, 0.75)
        pfrechetCopula(runif(5))
        
        grid2d()
        pfrechetCopula(grid2d())

