Transformed Copulas

SurvivalCopula(C,indices)

Computes the survival version of any copula on given indices. From a copula $C$ in dimension $d$, and some indices $i_1,...i_k$ in ${1,...,d}$, the survival copula associated simply reverses its arguments on chosen indices. For exemple, for $d=4$ and indices $(2,3)$, we have:

\[S(u_1,...u_4) = C(u_1,1-u_2,1-u3,u_4)\]

This constructor allows to derive new "survival" families. For exemple, in bivariate cases, this allows to do "rotations". The obtained models can be treated as the starting one, i.e. as a random vector in [0,1]^d with uniforms marginals.

References:

• [3] Nelsen, Roger B. An introduction to copulas. Springer, 2006.

subsetdims(C::Copula,dims)
subsetdims(D::SklarDist, dims)

If $(X_1,...,X_n)$ is the random vector corresponding to the model C or D, this returns the distribution on ( $X_i$ for i in dims), preserving the dependence structure between the dimensions in dims. There are specialized methods for some copulas.

SubsetCopula{d,CT}

Fields:

• C::CT - The copula
• dims::Tuple{Int64} - a Tuple representing which dimensions are used.

Constructor

SubsetCopula(C::Copula,dims)

This class allows to construct a random vector corresponding to a few dimensions of the starting copula. If $(X_1,...,X_n)$ is the random vector corresponding to the copula C, this returns the copula of ( $X_i$ for i in dims). The dependence structure is preserved. There are specialized methods for some copulas.