cauchy2d              package:fMultivar              R Documentation

_B_i_v_a_r_i_a_t_e _C_a_u_c_h_y _D_i_s_t_r_i_b_u_t_i_o_n

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

     Density, distribution function, and random  generation for the
     bivariate Cauchy  distribution.

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

     pcauchy2d(x, y = x, rho = 0)
     dcauchy2d(x, y = x, rho = 0)
     rcauchy2d(n, rho = 0)

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

       n: the number of random deviates to be generated, an integer
          value. 

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

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

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

     'pcauchy2d' 
      returns a two column matrix of probabilities for the bivariate 
     Cauchy distribution function.

     'dcauchy2d' 
      returns a two column matrix of densities for the bivariate 
     Cauchy distribution function.


     'rcauchy2d' 
      returns a two column matrix of random deviates generated from the
     bivariate Cauchy distribution function.

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

     Adelchi Azzalini for the underlying pnorm2d function, 
      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:

     ## Bivariate Cauchy Density:
        x = (-40:40)/10
        X = grid2d(x)
        z = dcauchy2d(X$x, X$y, rho = 0.5)
        Z = list(x = x, y = x, z = matrix(z, ncol = length(x)))
        persp(Z, theta = -40, phi = 30, col = "steelblue")

