copBasic (version 2.0.1)

level.curvesCOP2: 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 using the inverse of a copula by COPinv2.

Usage

level.curvesCOP2(cop=NULL, para=NULL, ploton=TRUE, lines=TRUE,
                 plotMW=FALSE, ramp=TRUE, delv=0.001, delt=0.10,
                 getlevel=NULL, ...)

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 Rto draw the lines;

plotMW

A logical to toggle to use abline() function in Rto 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 1000, 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 Rlist data structure; 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 Rlist.

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

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

Examples

level.curvesCOP2(cop=M, para=NULL, delt=.02) # Upper bounds copula