dcbb9 {mlCopulaSelection}R Documentation

BB9 copula density function

Description

Calculate the value of the BB9 density.

Usage

dcbb9(theta, delta, u, v)

Arguments

theta Parameter theta of the BB9, (1<theta).
delta Parameter delta of the BB9, (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 BB9 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<-dcbb9(1.5,1.5,0.75,0.6)

## The function is currently defined as
function(theta,delta,u,v)
{S<-delta-log(u);
T<-delta-log(v);
W<-S^(theta)+T^(theta)-delta^(theta);
C<-exp(-W^(1/theta)+delta);
DuS<--1/u;
DuW<-theta*S^(theta-1)*DuS;
DvT<--1/v;
DvW<-theta*T^(theta-1)*DvT;
densi<-C*(1/theta^2)*(W^(1/theta-1))^2*DvW*DuW+C*(-1/theta)*(1/theta-1)*W^(1/theta-2)*DvW*DuW
  }

[Package mlCopulaSelection version 1.3 Index]