dcbb1           package:mlCopulaSelection           R Documentation

_B_B_1 _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 BB1 density.

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

     dcbb1(theta, delta, u, v)

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

   theta: Parameter 'theta' of the BB1. (0<'theta') 

   delta: Parameter 'delta' of the BB1. (1<'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 BB1 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<-dcbb1(0.5,1.5,0.90,0.85)

     ## The function is currently defined as
     function(theta,delta,u,v)
     {S<-u^(-theta)-1;
     T<-v^(-theta)-1;-10**(4)
     W<-S^(delta)+T^(delta);
     DuS<-(-theta)*u^(-theta-1);
     DuW<-delta*S^(delta-1)*DuS;
     DvT<-(-theta)*v^(-theta-1);
     DvW<-delta*T^(delta-1)*DvT;
     densi<-(-1/(theta*delta))*(-1/theta-1)*(1+W^(1/delta))^(-1/theta-2)*(1/delta)*W^(1/delta-1)*DvW*W^(1/delta-1)*DuW-(1/(theta*delta))*(1+W^(1/delta))^(-1/theta-1)*(1/delta-1)*W^(1/delta-2)*DvW*DuW
       }

