dcbb7 {mlCopulaSelection}R Documentation

BB7 copula density function

Description

Calculate the value of the BB7 density.

Usage

dcbb7(theta, delta, u, v)

Arguments

theta Parameter theta of the BB7, (1<theta).
delta Parameter delta of the BB7, (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 BB7 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<-dcbb7(1.5,1.5,0.75,0.6)


## The function is currently defined as
function(theta,delta,u,v)
{WU<-(1-(1-u)^(theta))^(-delta);
        WV<-(1-(1-v)^(theta))^(-delta);
        duWU<-(-delta*theta)*(1-(1-u)^(theta))^(-delta-1)*(1-u)^(theta-1);
        dvWV<-(-delta*theta)*(1-(1-v)^(theta))^(-delta-1)*(1-v)^(theta-1);
        K<-WU+WV;
        duK<-duWU;
        dvK<-dvWV;
        S<-K-1;
        duS<-duK;
        dvS<-dvK;
        h<-1-S^(-1/delta);
        duh<-(1/delta)*S^(-1/delta-1)*duS;
        dvh<-(1/delta)*S^(-1/delta-1)*dvS;
        dvuh<-(1/delta)*(-1/delta-1)*(S)^(-1/delta-2)*(dvS)*(duS);
        densi<-(-1/theta)*(1/theta-1)*h^(1/theta-2)*dvh*duh-(1/theta)*h^(1/theta-1)*dvuh
        }

[Package mlCopulaSelection version 1.3 Index]