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 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, ...)

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 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.

Author

W.H. Asquith

References