elliptical2d            package:fMultivar            R Documentation

_B_i_v_a_r_i_a_t_e _E_l_l_i_p_t_i_c_a_l _D_e_n_s_i_t_i_e_s

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

     Density function for bivariate elliptical  distributions.

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

     delliptical2d(x, y = x, rho = 0, param = NULL, type = c("norm", "cauchy", "t", 
         "logistic", "laplace", "kotz", "epower"), output = c("vector", "list"))

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

  output: 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. 

   param: additional parameters to specify the bivariate density
          function. Only effective for the Kotz and Exponential Power
          distribution. For the Kotz distribution we can specify a
          numeric value, by default defined as 'param=c(r=sqrt(2))',
          and for the Exponential Power distribution a numeric vector,
          by default defined as 'param=c(r=sqrt(2)),s=1/2'. 

     rho: the correlation parameter, a numeric value ranging between 
          minus one and one, by default zero.      

    type: the type of the elliptical copula. A character string
          selected  from: '"norm"', '"cauchy"', '"t"', '"laplace"', 
          '"kotz"', or '"epower"'. 

    x, y: two numeric vectors defining the x and y coordinates. 


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

     'delliptical2d' 
      returns a two column matrix of densities for the selected
     bivariate  elliptical distribution function.

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

     Diethelm Wuertz for the Rmetrics R-port.

_R_e_f_e_r_e_n_c_e_s:

     Azzalini A., (2004); _The sn Package_; R Reference Guide available
     from www.r-project.org.

     Venables W.N., Ripley B.D., (2002);  _Modern Applied Statistics
     with S_, Fourth Edition, Springer.

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

     ## Kotz' Elliptical Density:
        x = (-40:40)/10
        X = grid2d(x)
        z = delliptical2d(X$x, X$y, rho = 0.5, type = "kotz")
        Z = list(x = x, y = x, z = matrix(z, ncol = length(x)))
        persp(Z, theta = -40, phi = 30, col = "steelblue")

