Compute the copula sections or the (partial) derivatives of copula sections of a copula (Nelsen, 2006, pp. 12--14). The horizontal section at \(V=a\) (a constant) is
$$t \mapsto \mathbf{C}(t,a)\mbox{, and}$$
the vertical section at \(U=a\) (a constant, with respect to \(V\) or wrtV=TRUE) is
$$t \mapsto \mathbf{C}(a,t)\mbox{.}$$
The partial derivatives of the copula sections are conditional cumulative distribution functions (see derCOP and derCOP2). The derivatives are constrained as
$$0 \le \frac{\delta}{\delta u}\mathbf{C}(u,v) \le 1\mbox{, and}$$
$$0 \le \frac{\delta}{\delta v}\mathbf{C}(u,v) \le 1\mbox{.}$$
sectionCOP(f, cop=NULL, para=NULL, wrtV=FALSE, dercop=FALSE, delt=0.005,
ploton=TRUE, lines=TRUE, xlab="NONEXCEEDANCE PROBABILITY", ...)An R
list is returned.
The nonexceedance probability along the section. The nomenclature \(t\) mimics Nelsen (2006) and is not the same as the \(u\) or \(v\);
The section of the copula or its derivative;
A text string declaring what the setting for wrtV was;
The provided value of nonexceedance probability; and
A logical stating whether the derivative of the section is seccop.
A single value of nonexceedance probability \(u\) or \(v\) along the horizontal \(U\) axis or vertical \(V\) axis of the unit square \(\mathcal{I}^2\);
A copula function;
Vector of parameters, if needed, to pass to the copula;
A logical to toggle between with respect to \(v\) or \(u\) (default). The default provides the vertical section whereas the horizontal comes from wrtV = TRUE;
A logical that triggers the derivative of the section;
The increment of the level curves to plot, defaults to 5-percent intervals;
A logical to toggle on the plot;
Draw the lines of diagonal to the current device;
A label for the x-axis title passed to plot() in R; and
Additional arguments to pass to the plot() and lines() functions in R.
W.H. Asquith
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
COP, diagCOP