level.curvesCOP: Compute and Plot Level Curves of a Copula V with respect to U
In copBasic: General Bivariate Copula Theory and Many Utility Functions

level.curvesCOP

R Documentation

Compute and Plot Level Curves of a Copula V with respect to U

Description

Compute and plot level curves or level sets of a copula for V with respect to U (Nelsen, 2006, pp. 12–13). The level curves at levels t \mapsto [0+\Delta t, 1-\Delta t, \Delta t] are 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. Plotting is provided by this function because level curves are such an important visual attribute of a copula and highly useful for pedagogic purposes. The above equation is implemented by the inverse of a copula using COPinv.

Usage

level.curvesCOP(cop=NULL, para=NULL, ploton=TRUE, lines=TRUE,
                plotMW=FALSE, ramp=TRUE, delu=0.001, delt=0.10,
                getlevel=NULL, silent=TRUE, ...)

Arguments

`cop`	A copula function;
`para`	Vector of parameters or other data structure, if needed, to pass to the copula;
`ploton`	A logical to toggle on the plot;
`lines`	A logical to toggle calls to the `lines()` function in R to draw the lines;
`plotMW`	A logical to toggle to use the `abline()` function in R to plot cross lines for the `\mathbf{M}` (`M`) and `\mathbf{W}` (`W`) copulas;
`ramp`	A logical to toggle whether the level curves are ramped in thickness according to the probability of the line. The argument can be used with a `lwd` setting through the `...` and can either be a constant, which will override the built-in ramp, or `lwd` can be defined as a function to replace the built-in ramp in terms of the probability;
`delu`	The increment for `\Delta u`. The default is 1 part in 1,000, which should often provide enough smoothness for many copulas in practice;
`delt`	The increment `\Delta t` for the level curves to plot, defaults to 10-percent intervals. If `delt=0.5`, then only the median plus the consequences of a defined `getlevel` is used. If `NULL`, then a sequence of `t` values is not made and only `getlevel` is used (if available);
`getlevel`	If defined, then it is inserted into the sequence of levels `t` and that level `t` `=` `getlevel` is returned in an R `list` data structure. If more than one level is desired, then instead of repeated calls to this function, the `joint.curvesCOP` function could be considered;
`silent`	The argument of the same name given over to `try()` wrapping the `try()` operation on forming sequences of `t` for the curves (see sources); and
`...`	Additional arguments to pass to the `lines()` function in R.

Value

Typically no values are returned because this function is used for its side effects, but the arguments can be such that the \{u, v\} for \mathbf{C}(u,v) = t are returned within an R list.

Author(s)

W.H. Asquith

References

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

Examples

## Not run: 
level.curvesCOP(cop=M, para=NULL, delt=0.02) # Upper bounds copula
## End(Not run)
## Not run: 
D <- level.curvesCOP(cop=P,   getlevel=0.56)
str(D) # empty
D <- level.curvesCOP(cop=P,   getlevel=0.5)
str(D) # contains stuff
D <- level.curvesCOP(cop=PSP, getlevel=0.8)
str(D) # contains stuff
## End(Not run)

copBasic documentation built on June 28, 2025, 1:08 a.m.