dcbb3 {mlCopulaSelection}R Documentation

BB3 copula density function

Description

Calculate the value of the BB3 density.

Usage

dcbb3(theta, delta, u, v)

Arguments

theta Parameter theta of the BB3, (0<theta).
delta Parameter delta of the BB3, (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 BB3 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<-dcbb3(1.5,1.5,0.75,0.6)

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

[Package mlCopulaSelection version 1.3 Index]