diagCOP {copBasic} | R Documentation |
The Diagonals of a Copula
Description
Compute the primary diagonal or alternatively the secondary diagonal (Nelsen, 2006, pp. 12 and 16) of copula .
The primary diagonal is defined as
and the secondary diagonal is defined as
Plotting is provided by this function because the diagonals are such important visual attributes of a copula. This function computes whole diagonals. If individual values are desired, then users are asked to use function calls along the diagonal such as COP(0.25,0.25, cop=P)
for the primary diagonal and COP(0.25,1-0.25, cop=P)
for the secondary diagonal, where for both examples the independence copula (;
P
) was chosen for purposes of clarification.
The is related to order statistics of the multivariate sample (here bivariate) (Durante and Sempi, 2015, p. 68). The probability for the maxima is
the probability for the minima is
Usage
diagCOP(cop=NULL, para=NULL, secondary=FALSE,
ploton=TRUE, lines=TRUE, delt=0.005, ...)
Arguments
cop |
A copula function; |
para |
Vector of parameters, if needed, to pass to the copula; |
secondary |
A logical to toggle the secondary diagonal; |
ploton |
A logical to toggle on the plot; |
lines |
Draw the lines of diagonal to the current device; |
delt |
The increment of the diagonal curve to plot, defaults to 0.5-percent intervals, which should be small enough to resolve fine curvature for many copulas in practice; and |
... |
Additional arguments to pass to the |
Value
An R list
of the values,
(primary) or
(secondary diagonal), along with a tag as to which diagonal is returned.
Author(s)
W.H. Asquith
References
Durante, F., and Sempi, C., 2015, Principles of copula theory: Boca Raton, CRC Press, 315 p.
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
See Also
Examples
## Not run:
# The primary diagonal of the W, P, M, and PSP copulas on the same plot
D <- diagCOP(cop=W, lwd=2)
D <- diagCOP(cop=P, lty=2, ploton=FALSE)
D <- diagCOP(cop=M, col=2, ploton=FALSE)
D <- diagCOP(cop=PSP, col=3, ploton=FALSE)
mtext("PRIMARY DIAGONAL OF SIMPLE COPULAS") # four primary diagonals
## End(Not run)
## Not run:
# The secondary diagonal of the W, P, M, and PSP copulas on the same plot
D <- diagCOP(cop=W, lwd=2, secondary=TRUE)
D <- diagCOP(cop=P, lty=2, secondary=TRUE, ploton=FALSE)
D <- diagCOP(cop=M, col=2, secondary=TRUE, ploton=FALSE)
D <- diagCOP(cop=PSP, col=3, secondary=TRUE, ploton=FALSE)
mtext("SECONDARY DIAGONAL OF SIMPLE COPULAS") # four secondary diagonals
## End(Not run)