copBasic (version 1.7.1)

diagCOP: The Diagonals of a Copula

Description

Compute the primary diagonal or alternatively the secondary diagonal (Nelsen, 2006, pp. 12 and 16) of copula $\mathbf{C}(u,v)$. The primary diagonal is defined as $$\mathbf{\delta}_\mathbf{C}(t) = \mathbf{C}(t,t)\mbox{,}$$ and the secondary diagonal is defined as $$\mathbf{\delta}^{\star}_\mathbf{C}(t) = \mathbf{C}(t,1-t)\mbox{.}$$ Plotting is provided by this function because the diagonals are such important visual attributes of a copula.

Usage

diagCOP(cop=NULL, para=NULL, secondary=FALSE,
        ploton=TRUE, lines=TRUE, delt=0.005, ...)

Arguments

cop

A copula function;

para

Vector of parameters, if needed, to pass to the copula;

secondary

A logical to toggle the secondary diagonal;

ploton

A logical to toggle on the plot;

lines

Draw the lines of diagonal to the current device;

delt

The increment of the level curves to plot, defaults to 5-percent intervals; and

...

Additional arguments to pass to the plot() and lines() functions of R.

Value

• An Rlist of the t values, $\mathbf{\delta}_\mathbf{C}(t,t)$ (primary) or $\mathbf{\delta}^{\star}_\mathbf{C}(t,1-t)$ (secondary diagonal), along with a tag as to which diagonal is returned.

References

Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.

See Also

diagCOPatf, COP, sectionCOP

Examples

# The primary diagonal of the W, P, M, and PSP copulas on the same plot
D <- diagCOP(cop=W,   lwd=2)
D <- diagCOP(cop=P,   lty=2, ploton=FALSE)
D <- diagCOP(cop=M,   col=2, ploton=FALSE)
D <- diagCOP(cop=PSP, col=3, ploton=FALSE)
mtext("PRIMARY DIAGONAL OF SIMPLE COPULAS")

# The secondary diagonal of the W, P, M, and PSP copulas on the same plot
D <- diagCOP(cop=W,   lwd=2, secondary=TRUE)
D <- diagCOP(cop=P,   lty=2, secondary=TRUE, ploton=FALSE)
D <- diagCOP(cop=M,   col=2, secondary=TRUE, ploton=FALSE)
D <- diagCOP(cop=PSP, col=3, secondary=TRUE, ploton=FALSE)
mtext("SECONDARY DIAGONAL OF SIMPLE COPULAS")