dcbb10           package:mlCopulaSelection           R Documentation

_B_B_1_0 _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 BB10 density.

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

     dcbb10(theta, delta, u, v)

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

   theta: Parameter 'theta' of the BB10, (0<'theta'<1).  

   delta: Parameter 'delta' of the BB10, (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 BB10 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<-dcbb10(1.5,1.5,0.75,0.6)


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

