copBasic (version 2.0.1)

level.setCOP: Compute a Level Set of a Copula V with respect to U

Description

Compute a level curve or level set of a copula for $V$ with respect to $U$ (Nelsen, 2006, pp. 12--13). The level curve at level $t$ is defined for $U \mapsto [0+\Delta u, 1-\Delta u, \Delta u]$ by $$t \mapsto \mathbf{C}(u{=}U, v)\mbox{,}$$ and solving for $v$. The function is largely a dispatcher to features implemented in level.curvesCOP.

Usage

level.setCOP(cop=NULL, para=NULL, getlevel=NULL, delu=0.001, lines=FALSE, ...)

Arguments

cop

A copula function;

para

Vector of parameters or other data structure, if needed, to pass to the copula;

getlevel

The level set for $t$;

delu

The increment for $\Delta u$. The default is 1 part in 1000, which should often provide enough smoothness for many copulas in practice;

lines

A logical that matches the argument of the same name in level.curvesCOP; and

...

Additional arguments to pass to the lines() function in R.

Value

• The level set for $t$ $=$ getlevel is returned.

concept

• level curves
• level curve
• level sets
• level set
• level contours
• level contour

References

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

See Also

level.setCOP2, level.curvesCOP

Examples

set <- level.setCOP(cop=PSP, getlevel=0.23, delu=0.005)
level.curvesCOP(cop=PSP)
lines(set$U, set$V, col=2, lwd=2) # manually draw the 23rd percentile
set <- level.setCOP(cop=PSP, para=3.1, getlevel=0.67, lines=TRUE, col=4, lwd=4)
# Notice the change in the lines argument and using levelsetCOP2 to draw.
mtext("Level Curves and Special Level Sets for PSP copula") #