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

dDiag {copula} | R Documentation

## 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, M., and McNeil, A. J. (2013). Archimedean Copulas in High Dimensions: Estimators and Numerical Challenges Motivated by Financial Applications. Journal de la Société Française 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")

[Package copula version 1.0-1 Index]