dcbb2 {mlCopulaSelection}R Documentation

BB2 copula density function

Description

Calculate the value of the BB2 density.

Usage

dcbb2(theta, delta, u, v)

Arguments

theta Parameter theta of the BB2, (0<theta).
delta Parameter delta of the BB2, (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 BB2 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<-dcbb2(0.5,0.5,0.75,0.6)

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

[Package mlCopulaSelection version 1.3 Index]