archmCopula | R Documentation |
Constructs an Archimedean copula class object with its corresponding parameter and dimension.
archmCopula(family, param = NA_real_, dim = 2, ...)
claytonCopula(param = NA_real_, dim = 2,
use.indepC = c("message", "TRUE", "FALSE"))
frankCopula(param = NA_real_, dim = 2,
use.indepC = c("message", "TRUE", "FALSE"))
gumbelCopula(param = NA_real_, dim = 2,
use.indepC = c("message", "TRUE", "FALSE"))
amhCopula(param = NA_real_, dim = 2,
use.indepC = c("message", "TRUE", "FALSE"))
joeCopula(param = NA_real_, dim = 2,
use.indepC = c("message", "TRUE", "FALSE"))
family |
a character string specifying the family of an Archimedean copula. Currently supported families are "clayton", "frank", "amh", "gumbel", and "joe". |
param |
number ( |
dim |
the dimension of the copula. |
... |
further arguments, passed to the individual creator
functions ( |
use.indepC |
a string specifying if the independence copula
|
archmCopula()
is a wrapper for claytonCopula()
,
frankCopula()
, gumbelCopula()
, amhCopula()
and
joeCopula
.
For the mathematical definitions of the respective Archimedean families,
see copClayton
.
For d = 2
, i.e. dim = 2
, the AMH, Clayton and Frank copulas
allow to model negative Kendall's tau (tau
) behavior via
negative \theta
, for AMH and Clayton
-1 \le \theta
, and for Frank
-\infty < \theta
.
The respective boundary cases are
\tau(\theta = -1) = -0.1817258
,
\tau(\theta = -1) = -1
,
\tau(\theta = -Inf) = -1
(as limit).
For the Ali-Mikhail-Haq copula family ("amhCopula"
), only the
bivariate case is available; however copAMH
has no such
limitation.
Note that in all cases except for Frank and AMH, and d = 2
and
theta < 0
, the densities (dCopula()
methods) are
evaluated via the dacopula
slot of the corresponding
acopula
-classed Archimedean copulas, implemented
in a numeric stable way without any restriction on the dimension d
.
Similarly, the (cumulative) distribution function
(“"the copula"” C()
) is evaluated via the corresponding
acopula
-classed Archimedean copula's functions in
the psi
and iPsi
slots.
An Archimedean copula object of class "claytonCopula"
,
"frankCopula"
, "gumbelCopula"
, "amhCopula"
, or "joeCopula"
.
R.B. Nelsen (2006), An introduction to Copulas, Springer, New York.
acopula
-classed Archimedean copulas, such as
copClayton
, copGumbel
, etc, notably for
mathematical definitions including the meaning of param
.
fitCopula
for fitting such copulas to data.
ellipCopula
, evCopula
.
clayton.cop <- claytonCopula(2, dim = 3)
## scatterplot3d(rCopula(1000, clayton.cop))
## negative param (= theta) is allowed for dim = 2 :
tau(claytonCopula(-0.5)) ## = -1/3
tauClayton <- Vectorize(function(theta) tau(claytonCopula(theta, dim=2)))
plot(tauClayton, -1, 10, xlab=quote(theta), ylim = c(-1,1), n=1025)
abline(h=-1:1,v=0, col="#11111150", lty=2); axis(1, at=-1)
tauFrank <- Vectorize(function(theta) tau(frankCopula(theta, dim=2)))
plot(tauFrank, -40, 50, xlab=quote(theta), ylim = c(-1,1), n=1025)
abline(h=-1:1,v=0, col="#11111150", lty=2)
## tauAMH() is function in our package
iTau(amhCopula(), -1) # -1 with a range warning
iTau(amhCopula(), (5 - 8*log(2)) / 3) # -1 with a range warning
ic <- frankCopula(0) # independence copula (with a "message")
stopifnot(identical(ic,
frankCopula(0, use.indepC = "TRUE")))# indep.copula withOUT message
(fC <- frankCopula(0, use.indepC = "FALSE"))
## a Frank copula which corresponds to the indep.copula (but is not)
frankCopula(dim = 3)# with NA parameters
frank.cop <- frankCopula(3)# dim=2
persp(frank.cop, dCopula)
gumbel.cop <- archmCopula("gumbel", 5)
stopifnot(identical(gumbel.cop, gumbelCopula(5)))
contour(gumbel.cop, dCopula)
amh.cop <- amhCopula(0.5)
u. <- as.matrix(expand.grid(u=(0:10)/10, v=(0:10)/10, KEEP.OUT.ATTRS=FALSE))
du <- dCopula(u., amh.cop)
stopifnot(is.finite(du) | apply(u. == 0, 1,any)| apply(u. == 1, 1,any))
## A 7-dim Frank copula
frank.cop <- frankCopula(3, dim = 7)
x <- rCopula(5, frank.cop)
## dCopula now *does* work:
dCopula(x, frank.cop)
## A 7-dim Gumbel copula
gumbelC.7 <- gumbelCopula(2, dim = 7)
dCopula(x, gumbelC.7)
## A 12-dim Joe copula
joe.cop <- joeCopula(iTau(joeCopula(), 0.5), dim = 12)
x <- rCopula(5, joe.cop)
dCopula(x, joe.cop)
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