dcbb6           package:mlCopulaSelection           R Documentation

_B_B_6 _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 BB6 density.

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

     dcbb6(t, d, u, v)

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

       t: Parameter 't' of the BB6, (1<'t').  

       d: Parameter 'd' of the BB6, (1<'d'). 

       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 BB6 for the parameters  't'  and  'd' 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<-dcbb6(1.5,1.5,0.75,0.6)


     ## The function is currently defined as
     function(t,d,u,v)
     {
             
       t19 = (d*t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d-1.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-1.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))-(t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**2*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(2./d-2.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(1./t-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-2.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))+(d*t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**2*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d-2.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(1./d-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-1.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))
       }

