copBasic (version 2.0.1)

level.curvesCOP: 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 using the inverse of a copula by COPinv.

Usage

level.curvesCOP(cop=NULL, para=NULL, ploton=TRUE, lines=TRUE,
                plotMW=FALSE, ramp=TRUE, delu=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 the 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;

delu

The increment for $\Delta u$. The default is 1 part in 1000, 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 i

getlevel

If defined, then it is inserted into the sequence of levels $t$ and that level $t$ $=$ getlevel is returned in an Rlist data structure. If more than one level is desired, then instead of repeated calls to this function, the

...

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

COPinv, level.curvesCOP2, level.setCOP, joint.curvesCOP

Examples

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