dcbb7           package:mlCopulaSelection           R Documentation

_B_B_7 _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 BB7 density.

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

     dcbb7(theta, delta, u, v)

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

   theta: Parameter 'theta' of the BB7, (1<'theta').  

   delta: Parameter 'delta' of the BB7, (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 BB7 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<-dcbb7(1.5,1.5,0.75,0.6)


     ## The function is currently defined as
     function(theta,delta,u,v)
     {WU<-(1-(1-u)^(theta))^(-delta);
             WV<-(1-(1-v)^(theta))^(-delta);
             duWU<-(-delta*theta)*(1-(1-u)^(theta))^(-delta-1)*(1-u)^(theta-1);
             dvWV<-(-delta*theta)*(1-(1-v)^(theta))^(-delta-1)*(1-v)^(theta-1);
             K<-WU+WV;
             duK<-duWU;
             dvK<-dvWV;
             S<-K-1;
             duS<-duK;
             dvS<-dvK;
             h<-1-S^(-1/delta);
             duh<-(1/delta)*S^(-1/delta-1)*duS;
             dvh<-(1/delta)*S^(-1/delta-1)*dvS;
             dvuh<-(1/delta)*(-1/delta-1)*(S)^(-1/delta-2)*(dvS)*(duS);
             densi<-(-1/theta)*(1/theta-1)*h^(1/theta-2)*dvh*duh-(1/theta)*h^(1/theta-1)*dvuh
             }

