ArchimedeanGenerator        package:fCopulae        R Documentation

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

     A collection and description of functions  concerned with the
     generator function for  the Archimedean copula and with functions
     for setting and checking the distributional parameters. 

     Functions:

       'evList'       Returns list of implemented Archimedean copulae,
       'archmParam'   Sets default parameters for an Archimedean copula,
       'archmRange'   returns the range of valid rho values,
       'archmCheck'   checks if rho is in the valid range,
       'Phi'          Computes generator Phi, inverse and derivatives,
       'PhiSlider'    displays interactively generator function,
       'Kfunc'        computes copula density and its inverse,
       'KfuncSlider'  displays interactively density function.

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

     archmList()
     archmParam(type = archmList())
     archmRange(type = archmList(), B = Inf)
     archmCheck(alpha, type = archmList())
           
     Phi(x, alpha = NULL, type = archmList(), inv = FALSE, deriv = paste(0:2))
     PhiSlider(B = 5)

     Kfunc(x, alpha = NULL, type = archmList(), inv = FALSE, lower = 1.0e-8)
     KfuncSlider(B = 5)

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

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

       B: [archmRange] - 
           the maximum slider menu value when the boundary value is
          infinite.  By default this is set to 'B=Inf'.
           [*Slider] - 
           the maximum slider menu value when the boundary value is
          infinite.  By default this is set to 'B=5'. 

   deriv: [Phi] - 
           an integer value. Should the function itself, 'deriv="0"', 
          or the first 'deriv="1"', or second 'deriv="2"' derivative 
          be evaluated? 

     inv: [Phi][Kfunc] - 
           a logical flag. Should the inverse function be computed? 

   lower: [Kfunc] - 
           a numeric value setting the lower bound for the internal
          root  finding function 'uniroot'. 

    type: [*archmCopula][Phi][Kfunc] - 
           the type of the Archimedean copula. A character string
          ranging  beween '"1"' and '"22"'. By default copula No. 1
          will  be chosen. 

       x: [Kfunc] - 
           a numeric value or vector ranging between zero and one.
           [Phi] - 
           a numeric value or vector. 

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

     The function 'Phi' returns a numeric vector with the values
     computed from the Archemedean generator, its derivatives, or its
     inverse. 

     The function 'Kfunc' returns 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:

       
     ## archmList -
        # Return list of implemented copulae:
        archmList()

