Produce a list containing dependence function of specified EV copula family, its derivatives and parameters bounds. Only Hussler-Reiss family is limited to two dimensions.
ldepPartition3D returns set of 5 dependence functions (see details).
depfun(name, ...)dep1(...)
depGalambos(...)
depGumbel(...)
depHuslerReiss(...)
depMax(power = 10, ...)
depTawn(dim = 2, ...)
depCC(depfun = list(dep1(),depGumbel()),
dparameters = lapply(depfun,
function(x) rep(list(NULL),max(1,length(x$parameters)))),
dim = 2)
depGCC(depfun=list(dep1(),depGumbel()),
dparameters = lapply(depfun,
function(x) rep(list(NULL),max(1,length(x$parameters)))),
dim = 2, symmetry = FALSE)
ldepPartition3D(power = 8)
numeric vector to be used whenever parameters of depfun are not supplied to procedure that use it, or as starting values in estimation
function of two arguments; the first is depfun argument, the another is depfun parameters
function; depfun first derivative
function; depfun second derivative
list. Correlation coefficient as function of copula parameter (coef), its inverse (icoef) and range (bounds). Available only for 1-parameter families.
numeric; parameters boundary
character; identification of depfun family
function; extract the combination parameters from the set of provided parameters and rescale them if not fulfilling inner conditions of the (general) convex combination
character. Code name for Pickands' dependence function, identical with the part after dep.
numeric. Parameter of Gumbel family dependence function, which approximates the weakest dependence function in order to bring smoothness.
numeric. Dimension (of copula) of random vector.
list of dependence function definition lists, also ldepPartition3D can be used.
list of dependence function parameters; defaults to list of NULLs which means the parameters are to be estimated.
logical. If TRUE, then GCC reduces to standard convex sum and depCC is used.
named arguments. Items of the dependence function definition list to be redefined.
Tomas Bacigal
Currently implemented families of EV copula dependence functions:
| family | dependence function \(A(t)=\) | domain | EV.case |
| 1 | \( 1 \) | \(\Pi\) | |
| Galambos | \(1 - (\sum_i t_i^{-p})^{-1/p} \) | [0,10] | 1(\(\Pi\)),Inf(M) |
| Gumbel-Hougaard | \((\sum_i(t_i^{p}))^{1/p}\) | [1,Inf] | 1(\(\Pi\)),Inf(M) |
| Husler-Reiss | \(t_1 \Phi(1/p + p \log(t_1/t_2)/2) + \atop + t_2 \Phi(1/p - p \log(t_1/t_2)/2)\) | [0,Inf] | 0(\(\Pi\)),Inf(M) |
| Max | \((\sum_i{t_i^{10}})^{1/10}\) | \(M\) | |
| Tawn | \(1 - \sum_i{p_i t_i} + (\sum_i{(p_i t_i)^{p_0}})^{1/p_0}\) | [1,Inf]x[0,1]x... | {1,0,...}(W),{Inf,1,...}(M) |
Since \(\sum_i t_i=1\) a dependence function accepts argument vector with the last element omitted.
Bacigál, T., Mesiar, R.: 3-dimensional Archimax copulas and their fitting to real data. In: COMPSTAT 2012, 20th International conference on computational statistics. Limassol,Cyprus,27.-31.8.2012. The International Statistical Institute, 81--88 (2012).
Gudendorf, G., Segers, J. (2010): Extreme-value copulas. In Copula Theory and Its Applications. Springer Berlin Heidelberg, 127-145.
Insightful Corp.: EVANESCE Implementation in S-PLUS FinMetrics Module (2002). https://faculty.washington.edu/ezivot/book/QuanCopula.pdf Cited 6th July 2013.
pCopula, generator, copula
## the following gives the same definition list
depGumbel()
depfun("Gumbel")
## any list item can be modified upon function call
depGumbel(parameters=2.2,upper=10)
## general convex combination of 5 basic depfuns that arise from
## partitioning method for 3 dimensions; it results in
## (3x5)-parametric Pickand's dependence function definition list
depGCC(depfun=ldepPartition3D(), dim = 3)
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