Dependence modelling with extreme copulas in cherry junction trees structures

Modelling extremal dependence across multiple variables remains a central challenge in multivariate statistics, particularly under heavy-tailed or bounded-tail behaviour. Traditional vine copulas, such as C-vine and D-vine constructions, provide flexible representations of pairwise dependencies but often fail to capture heterogeneous or asymmetric tail behaviour. To address this limitation, an extended Cherry Junction Tree (CJT) framework is developed that integrates extreme-value copulas (EVCs), allowing a more adaptable and interpretable characterisation of heavy-tailed dependencies. A recursive formulation is derived for the CJT density and its tail dependence coefficients, facilitating scalability to higher dimensions. Simulation studies with Weibull, Gumbel, and Fréchet margins, together with an application to Swiss rainfall extremes, demonstrate superior tail sensitivity and improved model fit compared with classical vine structures. The proposed CJT–EV copula framework provides a robust and flexible approach for analyzing complex multivariate dependencies in extreme-value contexts.