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

In wasquith/copBasic: General Bivariate Copula Theory and Many Utility Functions

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 1,000, which should often in practice provide enough smoothness for many copulas;
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.

Author(s)

W.H. Asquith

References

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

See Also

level.setCOP2, level.curvesCOP

Examples

## Not run: 
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") #
## End(Not run)

wasquith/copBasic documentation built on Dec. 13, 2024, 6:39 p.m.