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 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, ...)

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.

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;
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.

Author

W.H. Asquith

References