3 Archimedean Copulae

Here is a review of existing methods. Need to double-check an actual book or some other literature on archimedean copulae, especially when it comes to domain of the association parameter \(\theta\).

3.1 Ali-Mikhail-Haq Copula

\(\theta \in [0, 1)\)

3.2 Clayton Copula

\(\theta \in (0, \infty)\). For dimension \(d = 2\), \(\theta \in (-1, \infty)\) is admissible.

3.3 Frank Copula

\(\theta \in (-\infty, +\infty)\)

3.4 Gumbel Copula

\(\theta \in [1, \infty)\)

3.5 Joe Copula

\(\theta \in [1, \infty)\)