dcbb4           package:mlCopulaSelection           R Documentation

_B_B_4 _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 BB4 density.

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

     dcbb4(theta, delta, u, v)

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

   theta: Parameter 'theta' of the BB4, (0<'theta').  

   delta: Parameter 'delta' of the BB4, (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 BB4 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<-dcbb4(1.5,1.5,0.75,0.6)

     ## The function is currently defined as
     function(theta,delta,u,v)
     {VV<-(u^(-theta)-1)^(-delta);
             WW<-(v^(-theta)-1)^(-delta);
             h<-VV+WW;
             S<-u^(-theta)+v^(-theta)-1;
             duh<-delta*theta*u^(-theta-1)*(u^(-theta)-1)^(-delta-1);
             dvh<-delta*theta*v^(-theta-1)*(v^(-theta)-1)^(-delta-1);
             duS<-(-theta)*u^(-theta-1);
             dvS<-(-theta)*v^(-theta-1);
             densi<-(1/theta)*(1/theta+1)*(S-h^(-1/delta))^(-1/theta-2)*(dvS+1/delta*h^(-1/delta-1)*dvh)*(duS+1/delta*h^(-1/delta-1)*duh)+(-1/theta)*(S-h^(-1/delta))^(-1/theta-1)*((-1/delta)*(1/delta+1)*(h)^(-1/delta-2)*dvh*duh)
             }

