Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications, however, extremes are intrinsically multivariate, requiring models that capture both marginal tail behaviours and joint extremal dependencies. Under asymptotic dependence, the multivariate GP distribution represents a suitable modelling family, but when asymptotic independence arises, sub-asymptotic models are needed. In this work, we propose and study a flexible sub-asymptotic parametric class to model bivariate threshold exceedances. Our new model accommodates a broad range of tail dependence behaviours and contains the standardised multivariate GP distribution as a limiting case while retaining margins that converge to univariate GP tails. Our formulation allows extremal dependence to evolve naturally with the marginal parameters on the original data scale, facilitating direct computation and interpretation of failure probabilities. Model inference is done via a likelihood-free neural Bayes estimation approach, with tailored prior specifications. An extensive simulation study and an application to Belgian rainfall extremes illustrate the estimation framework and the flexibility of the model.

翻译：极值理论为量化罕见事件风险提供了统计框架，其中广义帕累托分布是单变量阈值超出的经典极限模型。然而在许多应用中，极值本质上是多元的，需要同时捕捉边际尾部行为与联合极值依赖的模型。在渐近依赖条件下，多元广义帕累托分布构成了合适的建模族，但当出现渐近独立时，则需要采用次渐近模型。本研究提出并探索了一类灵活的次渐近参数模型用于双变量阈值超出建模。新模型能容纳广泛的尾部依赖行为，并以标准化多元广义帕累托分布为极限情形，同时保持边缘分布收敛至单变量广义帕累托尾部。其构建方式允许极值依赖随原始数据尺度上的边际参数自然演变，便于失效概率的直接计算与解释。模型推断采用无似然神经贝叶斯估计方法，并配以特定先验设定。通过大规模模拟研究与比利时极端降水的实际应用案例，验证了估计框架的有效性及模型的灵活性。