copBasic (version 1.7.1)

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. The above equation is implemented as 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 to draw the lines;

plotMW

A logical to toggle to use abline to plot cross lines for the M and 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 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 i

getlevel

If defined, then it is inserted into the sequence of levels $t$ and that level $t$ $=$ getlevel is returned in a list data structure; and

...

Additional arguments to pass to the lines() function of 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

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