clayton.rng.evd

Multivariate extreme value copula or, more generally, extreme value distribution are max-stable random vector with generalized extreme value margins and we may write

\[\mathbb{P}\{ \mathbf{X} \leq \mathbf{x} \} = \exp\{-\Lambda(E \setminus [\mathbf{0}, \mathbf{x}])\},\]

where \(\Lambda\) is a Radon measure on the cone \(E = [0,\infty]^d \setminus \mathbf{0}\). This dependendence structure can be translated with the classical notion of copula, \(C\) is an extreme value copula if

\[C(u) = \exp\{-\ell(-\ln(u_1), \dots, -\ln(u_d))\}, 0 < u_j \leq 1,\]

where \(\ell\) is the stable tail dependence function.

Structure :

• Extreme value copula (Extreme) from clayton.rng.base

  • Logistic model (Logistic)

  • Asymmetric logistic model (AsymmetricLogistic)

  • Husler Reiss (HuslerReiss)

  • Asymmetric negative logistic (AsyNegLog)

  • Asymmetric mixed (AsyMix)

  • t-Extreme Value (TEV)

  • Bilogistic model (Bilog)

Classes

AsyMix([theta, psi1, n_sample, dim])	Class for asymmetric mixed model.
AsyNegLog([theta, psi1, psi2, n_sample, dim])	Class for asymmetric negative logistic copula model.
AsymmetricLogistic([theta, n_sample, dim, asy])	Class for multivariate asymmetric logistic copula model.
Bilog([theta, n_sample, dim])	Class for bilogistic distribution model Smith (1990).
HuslerReiss([sigmat, n_sample, dim])	Class for Husler Reiss copula model.
Logistic([theta, n_sample, dim])	Class for multivariate Logistic copula model.
TEV([sigmat, psi1, n_sample, dim])	Class for t extreme value model.