ArchimedeanCopulae         package:fCopulae         R Documentation

_B_i_v_a_r_i_a_t_e _A_r_c_h_i_m_e_d_e_a_n _C_o_p_u_l_a_e

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

     A collection and description of functions to  investigate
     bivariate Archimedean copulae.  

     Archimedean Copulae Functions:

       'rarchmCopula'  Generates Archimedean copula variates,
       'parchmCopula'  computes Archimedean copula probability,
       'darchmCopula'  computes Archimedean copula density,
       'rarchmSlider'  displays interactive plots of variates,
       'parchmSlider'  displays interactive plots of probability,
       'darchmSlider'  displays interactive plots of density.

     Special Copulae Functions:

       'rgumbelCopula'  Generates Gumbel copula variates,
       'pgumbelCopula'  computes Gumbel copula probability,
       'dgumbelCopula'  computes Gumbel copula density.

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

     rarchmCopula(n, alpha = NULL, type = archmList())
     parchmCopula(u = 0.5, v = u, alpha = NULL, type = archmList(), output = 
         c("vector", "list"), alternative = FALSE )
     darchmCopula(u = 0.5, v = u, alpha = NULL, type = archmList(), output = 
         c("vector", "list"), alternative = FALSE )
        
     rarchmSlider(B = 10) 
     parchmSlider(type = c("persp", "contour"), B = 10)
     darchmSlider(type = c("persp", "contour"), B = 10)

     rgumbelCopula(n, alpha = 2)
     pgumbelCopula(u = 0.5, v = u, alpha = 2, output = c("vector", "list"))
     dgumbelCopula(u = 0.5, v = u, alpha = 2, output = c("vector", "list"))

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

   alpha: [Phi*][*archmCopula] - 
           the parameter of the Archemedean copula. A numerical value. 

alternative: [*Copula] - 
           Should the probability be computed alternatively ... 

       B: [*Slider] - 
           the maximum slider menu value when the boundary value is
          infinite.  By default this is set to 10. 

       n: [rarchmCopula] - 
                    the number of random deviates to be generated, an
          integer value. 

  output: [*archmCopula] - 
           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: [*archmCopula] - 
           the type of the Archimedean copula. A character string
          ranging  beween '"1"' and '"22"'. By default copula No. 1
          will  be chosen.
           [*archmSlider] - 
           the type of the plot. A charcter string either specifying a 
          perspective or contour plot. 

    u, v: [*archmCopula] - 
           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'. 

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

     The function 'pcopula' returns a numeric matrix of probabilities 
     computed at grid positions 'x'|'y'. 

     The function 'parchmCopula' returns a numeric matrix with values
     computed for the Archemedean copula. 

     The function 'darchmCopula' returns a numeric matrix with values
     computed for thedensity of the Archemedean copula. 

     The functions 'Phi*' return a numeric vector with the values
     computed from the Archemedean generator, its derivatives, or its
     inverse. 

     The functions 'cK' and {cKInv} return a numeric vector with the 
     values of the density and inverse for Archimedian copulae.

_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 default Normal Copula:
        # contour(pcopula())

