| dcbb4 {mlCopulaSelection} | R Documentation |
Calculate the value of the BB4 density.
dcbb4(theta, delta, u, v)
theta |
Parameter theta of the BB4, (0<theta). |
delta |
Parameter delta of the BB4, (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) |
value of de density BB4 for the parameters theta and delta on ( u , v )
Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP
Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.
res<-dcbb4(1.5,1.5,0.75,0.6)
## The function is currently defined as
function(theta,delta,u,v)
{VV<-(u^(-theta)-1)^(-delta);
WW<-(v^(-theta)-1)^(-delta);
h<-VV+WW;
S<-u^(-theta)+v^(-theta)-1;
duh<-delta*theta*u^(-theta-1)*(u^(-theta)-1)^(-delta-1);
dvh<-delta*theta*v^(-theta-1)*(v^(-theta)-1)^(-delta-1);
duS<-(-theta)*u^(-theta-1);
dvS<-(-theta)*v^(-theta-1);
densi<-(1/theta)*(1/theta+1)*(S-h^(-1/delta))^(-1/theta-2)*(dvS+1/delta*h^(-1/delta-1)*dvh)*(duS+1/delta*h^(-1/delta-1)*duh)+(-1/theta)*(S-h^(-1/delta))^(-1/theta-1)*((-1/delta)*(1/delta+1)*(h)^(-1/delta-2)*dvh*duh)
}