dcbb3           package:mlCopulaSelection           R Documentation

_B_B_3 _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 BB3 density.

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

     dcbb3(theta, delta, u, v)

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

   theta: Parameter 'theta' of the BB3, (0<'theta').  

   delta: Parameter 'delta' of the BB3, (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 BB3 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<-dcbb3(1.5,1.5,0.75,0.6)

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

