dcbb9           package:mlCopulaSelection           R Documentation

_B_B_9 _c_o_p_u_l_a _d_e_n_s_i_t_y _f_u_n_c_t_i_o_n

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

     Calculate the value of the BB9 density.

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

     dcbb9(theta, delta, u, v)

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

   theta: Parameter 'theta' of the BB9, (1<'theta').  

   delta: Parameter 'delta' of the BB9, (0<'delta'). 

       u: First coordenate where de density will be evaluated.
          (0<'u'<1)

       v: Second coordenate where de density will be evaluated.
          (0<'v'<1)

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

     value of de density BB9 for the parameters  'theta'  and  'delta'
     on ( 'u' ,  'v' )

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

     Jesus Garcia, IMECC-UNICAMP and  Veronica Gonzalez-Lopez,
     IMECC-UNICAMP

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

     Joe, H., (1997). Multivariate Models and Dependence Concepts. 
     Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

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

     res<-dcbb9(1.5,1.5,0.75,0.6)

     ## The function is currently defined as
     function(theta,delta,u,v)
     {S<-delta-log(u);
     T<-delta-log(v);
     W<-S^(theta)+T^(theta)-delta^(theta);
     C<-exp(-W^(1/theta)+delta);
     DuS<--1/u;
     DuW<-theta*S^(theta-1)*DuS;
     DvT<--1/v;
     DvW<-theta*T^(theta-1)*DvT;
     densi<-C*(1/theta^2)*(W^(1/theta-1))^2*DvW*DuW+C*(-1/theta)*(1/theta-1)*W^(1/theta-2)*DvW*DuW
       }

