dcbb4 {mlCopulaSelection}R Documentation

BB4 copula density function

Description

Calculate the value of the BB4 density.

Usage

dcbb4(theta, delta, u, v)

Arguments

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

value of de density BB4 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

Examples

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)
        }

[Package mlCopulaSelection version 1.3 Index]