ArchimedeanDependency        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:

       'archmTau'        Computes Kendall's tau for Archimedean copulae,
       'archmRho'        computes Spearman's rho for Archimedean copulae,
       'archmTailCoeff'  computes tail dependence for Archimedean copulae,
       'archmTailPlot'   plots tail dependence for Archimedean copulae.

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

        
     archmTau(alpha = NULL, type = archmList(), lower = 1.0e-10)
     archmRho(alpha = NULL, type = archmList(), method = c("integrate2d", "adapt"), 
         error = 1.0e-5)
         
     archmTailCoeff(alpha = NULL, type = archmList())
     archmTailPlot(alpha = NULL, type = archmList(), tail = c("Upper", "Lower"))

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

   alpha: the parameter of the Archemedean copula. A numerical value. 

   error: [archmRho] - 
           the error bound to be achieved by the 'integrate2d' 
          integration formula. A numeric value, by default
          'error=1.0e-5'. 

   lower: [archmTau] - 
           a numeric value setting the lower bound for the internal
          integration function 'integrate'. 

    tail: [archmTailPlot] - 
           a character string, either '"Upper"' or '"Lower"' denoting 
          which of the two tails should be displayed. By default the
          upper tail dependence will be considered. 

    type: the type of the Archimedean copula. A character string
          ranging  beween '"1"' and '"22"'. By default copula No. 1
          will  be chosen. 

  method: [archmRho] - 
                    a character string that determines which
          integration method should be  used, either '"integrate2d"' or
          '"adapt"'. If the second method is selected the contributed R
          package '"adapt"' is  required. 

_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())

