clayton.rng.base

A multivariate copula \(C : [0,1]^d \mapsto [0,1]\) of a d-dimensional random vector \(\mathbf{X}\) allows us to separate the effect of dependence from the effect of the marginal distributions such as:

\[\mathbb{P}\{ X_1 \leq x_1, \dots, X_d \leq x_d \} = C( \mathbb{P}\{X_1 \leq x_1\}, \dots, \mathbb{P} \{X_d \leq x_d\}),\]

where \((x_1,\dots,x_d) \in \mathbb{R}^d\). The main consequence of this identity is that the copula completely characterizes the stochastic dependence between the margins of \(\mathbf{X}\).

Structure :

• Multivariate copula (Multivariate)

  • Archimedean copula (clayton.rng.archimedean)

  • Extreme value copula (clayton.rng.evd)

Classes

Archimedean([theta, n_sample, dim])	Base class for multivariate archimedean copulas.
CopulaTypes(value)	Available multivariate copula
Extreme([n_sample, dim])	Base class for multivariate extreme value copulas.
Multivariate([n_sample, dim])	Base class for multivariate copulas.