mixCopula-class: Class '"mixCopula"' of Copula Mixtures
In copula: Multivariate Dependence with Copulas

mixCopula-class

R Documentation

Class `"mixCopula"` of Copula Mixtures

Description

The class "mixCopula" is the class of all finite mixtures of copulas.

These are given by (a list of) m “arbitrary” copulas, and their respective m non-negative probability weights.

Objects from the Class

Objects are typically created by mixCopula().

Slots

w:: Object of class "mixWeights", basically a non-negative numeric vector of length, say m, which sums to one.
cops:: Object of class "parClist", a list of (parametrized) copulas, "parCopula".

Extends

Class "parCopula", directly. Class "Copula", by class "parCopula", distance 2.

Methods

dim: signature(x = "mixCopula"): dimension of copula.
rho: signature(x = "mixCopula"): Spearman's rho of copula x.
lambda: signature(x = "mixCopula"): lower and upper tail dependecies lambda, (\lambda[L],\lambda[U]), of the mixture copula.

Note

As the probability weights must some to one (1), which is part of the validity (see validObject) of an object of class "mixWeights", the number of “free” parameters inherently is (at most) one less than the number of mixture components m.

Because of that, it does not make sense to fix (see fixParam or fixedParam<-) all but one of the weights: Either all are fixed, or at least two must be free. Further note, that the definition of free or fixed parameters, and the meaning of the methods (for mixCopula) of getTheta, setTheta and fixedParam<- will probably change in a next release of package copula, where it is planned to use a reparametrization better suited for fitCopula.