dcbb5 {mlCopulaSelection}R Documentation

BB5 copula density function

Description

Calculate the value of the BB5 density.

Usage

dcbb5(theta, delta, u, v)

Arguments

theta Parameter theta of the BB5, (1<theta).
delta Parameter delta of the BB5, (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 BB5 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<-dcbb5(1.5,1.5,0.75,0.6)

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

[Package mlCopulaSelection version 1.3 Index]