level.curvesCOP2: Compute and Plot Level Curves of a Copula U with respect to V

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

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

Description

Compute and plot level curves or level sets of a copula for U with respect to V (Nelsen, 2006, pp. 12–13). The level curves at a levels t \mapsto [0+\Delta t, 1-\Delta t, \Delta t] are defined for V \mapsto [0+\Delta v, 1-\Delta v, \Delta v] by

t = \mathbf{C}(u, v=V)\mbox{,}

and solving for u. 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 COPinv2.

Usage

level.curvesCOP2(cop=NULL, para=NULL, ploton=TRUE, lines=TRUE,
                 plotMW=FALSE, ramp=TRUE, delv=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 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;
delv	The increment of \Delta v. The default is 1 part in 1,000, which should often provide enough smoothness for many copulas in practice;
delt	The increment of \Delta t for the level curves to plot, defaults to 10-percent intervals;
getlevel	If defined and level exists upon stepping through using delt, then the level curve at the getlevel is returned in an R list data structure;
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.

See Also

COPinv2, level.curvesCOP, level.setCOP2, joint.curvesCOP2

Examples

## Not run: 
level.curvesCOP2(cop=M, para=NULL, delt=0.02) # Upper bounds copula
## End(Not run)

wasquith/copBasic documentation built on Dec. 30, 2024, 9:58 a.m.