copula: rotCopula – R documentation

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rotCopula

Construction and Class of Rotated aka Reflected Copulas

Description

Constructs a “reflected” or “rotated” copula from an initial copula and a vector of logicals indicating which dimension to “flip”.

Usage

rotCopula(copula, flip = TRUE)

Arguments

`copula`	an object of class `"Copula"`.
`flip`	`logical` vector (of length 1 or `dim(copula)`) indicating which dimension should be “flipped”; by default, all the components are flipped, implying that the resulting copula is the “survival copula”.

Value

A “rotated” or “reflected” copula object of class "rotCopula".

Slots

of a "rotCopula" object

copula:: Object of class "copula".
flip:: logical vector of length d (the copula dimension) specifying which margins are flipped; corresponds to the flip argument of rotCopula().
dimension:: the copula dimension d, an integer.
parameters:: numeric vector specifying the parameters.
param.lowbnd, and param.upbnd:: numeric vector of the same length as parameters, specifying (component wise) bounds for each of the parameters.
param.names:: character vector (of same length as parameters) with parameter names.
fullname:: deprecated; a character string describing the rotated copula.

Note

When there are an even number of flips, the resulting copula can be seen as a rotated version of copula. In the other cases, e.g., flip = c(FALSE,TRUE) in 2d, it is rather a a reflected or “mirrored” copula.

Examples

## Two-dimensional examples: First the Clayton(3) survival copula:
survC <- rotCopula(claytonCopula(3)) # default: flip = 'all TRUE'
contourplot2(survC, dCopula)

## Now, a reflected Clayton copula:
r10C  <- rotCopula(claytonCopula(3), flip = c(TRUE, FALSE))

contourplot2(r10C, dCopula, nlevels = 20, main = "dCopula(<rotCopula>)")
contourplot2(r10C, pCopula, nlevels = 20, main = "pCopula(<rotCopula>)")
rho(r10C)
tau(r10C) # -0.6

n <- 1000
u <- rCopula(n, r10C)
rho.n <- cor(u[,1], u[,2], method = "spearman")
tau.n <- cor(u[,1], u[,2], method = "kendall")

## "Calibration"
rc. <- rotCopula(claytonCopula(), flip = c(TRUE, FALSE))
iRho(rc., rho.n)
iTau(rc., tau.n)

## Fitting
fitCopula(rc., data = pobs(u), method = "irho")
fitCopula(rc., data = pobs(u), method = "itau")
fitCopula(rc., data = pobs(u), method = "mpl")

## Goodness-of-fit testing -- the first, parametric bootstrap, is *really* slow
## Not run: gofCopula(rc., x = u)
gofCopula(rc., x = u, simulation = "mult")

## A four-dimensional example: a rotated Frank copula
rf <- rotCopula(frankCopula(10, dim = 4),
                flip = c(TRUE, FALSE, TRUE, FALSE))

n <- 1000
u <- rCopula(n, rf)
splom2(u)

pCopula(c(0.6,0.7,0.6,0.8), rf)
C.n(cbind(0.6,0.7,0.6,0.8),  u)

## Fitting
(rf. <- rotCopula(frankCopula(dim=4),
                  flip = c(TRUE, FALSE, TRUE, FALSE)))
## fitCopula(rf., data = pobs(u), method = "irho")
## FIXME above: not related to rotCopula but frankCopula
fitCopula(rf., data = pobs(u), method = "itau")
fitCopula(rf., data = pobs(u), method = "mpl")

## Goodness-of-fit testing (first ("PB") is really slow, see above):
## Not run: gofCopula(rf., x = u)
gofCopula(rf., x = u, simulation = "mult") # takes 3.7 sec [lynne, 2015]

copula

Multivariate Dependence with Copulas

v1.0-1

GPL (>= 3) | file LICENCE

Authors

Marius Hofert [aut] (<https://orcid.org/0000-0001-8009-4665>), Ivan Kojadinovic [aut] (<https://orcid.org/0000-0002-2903-1543>), Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Jun Yan [aut] (<https://orcid.org/0000-0003-4401-7296>), Johanna G. Nešlehová [ctb] (evTestK(), <https://orcid.org/0000-0001-9634-4796>), Rebecca Morger [ctb] (fitCopula.ml(): code for free mixCopula weight parameters)

Initial release

2020-12-07