dcbb1 {mlCopulaSelection}R Documentation

BB1 copula density function

Description

Calculate the value of the BB1 density.

Usage

dcbb1(theta, delta, u, v)

Arguments

theta Parameter theta of the BB1. (0<theta)
delta Parameter delta of the BB1. (1<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 BB1 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<-dcbb1(0.5,1.5,0.90,0.85)

## The function is currently defined as
function(theta,delta,u,v)
{S<-u^(-theta)-1;
T<-v^(-theta)-1;-10**(4)
W<-S^(delta)+T^(delta);
DuS<-(-theta)*u^(-theta-1);
DuW<-delta*S^(delta-1)*DuS;
DvT<-(-theta)*v^(-theta-1);
DvW<-delta*T^(delta-1)*DvT;
densi<-(-1/(theta*delta))*(-1/theta-1)*(1+W^(1/delta))^(-1/theta-2)*(1/delta)*W^(1/delta-1)*DvW*W^(1/delta-1)*DuW-(1/(theta*delta))*(1+W^(1/delta))^(-1/theta-1)*(1/delta-1)*W^(1/delta-2)*DvW*DuW
  }

[Package mlCopulaSelection version 1.3 Index]