depfun {acopula} | R Documentation |
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)
name |
character. Code name for Pickands' dependence function, identical with the part after |
power |
numeric. Parameter of Gumbel family dependence function, which approximates the weakest dependence function in order to bring smoothness. |
dim |
numeric. Dimension (of copula) of random vector. |
depfun |
list of dependence function definition lists, also |
dparameters |
list of dependence function parameters; defaults to list of |
symmetry |
logical. If TRUE, then GCC reduces to standard convex sum and |
... |
named arguments. Items of the dependence function definition list to be redefined. |
Currently implemented families of EV copula dependence functions:
family | dependence function A(t)= | domain | EV.case |
1 | 1 | Π | |
Galambos | 1-sum(t^{-p})^{-1/p} | [0,10] | 1(Π),Inf(M) |
Gumbel-Hougaard | sum(t^p)^{1/p} | [1,Inf] | 1(Π),Inf(M) |
Husler-Reiss | t[1]*pnorm(1/p+p*log(t[1]/t[2])/2)+t[2]*pnorm(1/p-p*log(t[1]/t[2])/2) | [0,Inf] | 0(Π),Inf(M) |
Max | sum(t^10)^(1/10) | M | |
Tawn | 1 - sum(p[-1]*t) + sum((p[-1]*t)^p[1])^(1/p[1]) | [1,Inf]x[0,1]x... | {1,0,...}(W),{Inf,1,...}(M) |
Since sum(t)=1 a dependence function accepts argument vector with the last element omitted.
parameters |
numeric vector to be used whenever parameters of depfun are not supplied to procedure that use it, or as starting values in estimation |
dep |
function of two arguments; the first is depfun argument, the another is depfun parameters |
dep.der |
function; depfun first derivative |
dep.der2 |
function; depfun second derivative |
kendall,spearman |
list. Correlation coefficient as function of copula parameter ( |
lower,upper |
numeric; parameters boundary |
id |
character; identification of depfun family |
combpars,rescalepars |
function; extract the combination parameters from the set of provided parameters and rescale them if not fulfilling inner conditions of the (general) convex combination |
Tomas Bacigal
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). faculty.washington.edu/ezivot/book/QuanCopula.pdf Cited 6th July 2013.
## 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)