| dcbb5 {mlCopulaSelection} | R Documentation |
Calculate the value of the BB5 density.
dcbb5(theta, delta, u, v)
theta |
Parameter theta of the BB5, (1<theta). |
delta |
Parameter delta of the BB5, (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 BB5 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<-dcbb5(1.5,1.5,0.75,0.6)
## The function is currently defined as
function(theta,delta,u,v)
{t<-(-log(u))^(-theta*delta)+(-log(v))^(-theta*delta);
dut<-(theta*delta/u)*(-log(u))^(-theta*delta-1);
dvt<-(theta*delta/v)*(-log(v))^(-theta*delta-1);
S<-(-log(u))^(theta)+(-log(v))^(theta);
duS<-(-theta/u)*(-log(u))^(theta-1);
dvS<-(-theta/v)*(-log(v))^(theta-1);
h<-S-t^(-1/delta);
duh<-duS+(1/delta)*(t)^(-1/delta-1)*(dut);
dvh<-dvS+(1/delta)*(t)^(-1/delta-1)*(dvt);
dvuh<--1/delta*(1/delta+1)*t^(-1/delta-2)*dut*dvt;
densi<-exp(-h^(1/theta))*(1/theta)^2*(h^(1/theta-1))^2*dvh*duh+exp(-h^(1/theta))*(-1/theta)*(1/theta-1)*h^(1/theta-2)*dvh*duh+exp(-h^(1/theta))*(-1/theta)*h^(1/theta-1)*dvuh
}