copula (version 0.999-13)

dDiag: Density of the Diagonal of (Nested) Archimedean Copulas

Description

Evaluate the density of the diagonal of a $d$-dimensional (nested) Archimedean copula. Note that the diagonal of a copula is a cumulative distribution function. Currently, only Archimedean copulas are implemented.

Usage

dDiag(u, cop, log=FALSE)

Arguments

u

a numeric vector of evaluation points.

cop

a (nested) Archimedean copula object of class "outer_nacopula". This also determines the dimension via the comp slot

log

logical indicating if the log of the density of the diagonal should be returned instead of just the diagonal density.

Value

• A numeric vector containing the values of the density of the diagonal of the Archimedean copula at u.

References

Hofert, M., Mächler{Maechler}, M., and McNeil, A. J. (2013). Archimedean Copulas in High Dimensions: Estimators and Numerical Challenges Motivated by Financial Applications. Journal de la Socié{e}té{e} Franç{c}aise de Statistique 154(1), 25--63.

See Also

acopula class, dnacopula.

Examples

th. <- c(0.1, 0.2, 0.5, 0.8, 1.4, 2., 5.)
curve(dDiag(x, cop=onacopulaL("Clayton", list(th.[1], 1:3))), 0, 1,
      n=1000, ylab="dDiag(x, *)", main="Diagonal densities of Clayton")
abline(h=0, lty=3)
for(j in 2:length(th.))
  curve(dDiag(x, cop=onacopulaL("Clayton", list(th.[j], 1:3))), add=TRUE,
	     col=j, n=1000)
legend("topleft", do.call(expression, lapply(th., function(th)
                                 substitute(theta == TH, list(TH=th)))),
       lty = 1, col=seq_along(th.), bty="n")