This paper introduces a class of copula models for spatial data, based on multivariate Pareto-mixture distributions. We explore the tail properties of these models, demonstrating their ability to capture both tail dependence and asymptotic independence, as well as the tail asymmetry frequently observed in real-world data. The proposed models also offer flexibility in accounting for permutation asymmetry and can effectively represent both the bulk and extreme tails of the distribution. We consider special cases of these models with computationally tractable likelihoods and present an extensive simulation study to assess the finite-sample performance of the maximum likelihood estimators. Finally, we apply our models to analyze a temperature dataset, showcasing their practical utility.

翻译：本文基于多元帕累托混合分布，提出了一类适用于空间数据的连接函数模型。我们探讨了这些模型的尾部性质，证明了其能够同时捕捉尾部依赖性与渐近独立性，以及实际数据中常见的尾部不对称性。所提出的模型在考虑置换不对称性方面具有灵活性，并能有效表征分布的总体部分与极端尾部。我们研究了这些模型中具有计算可行似然函数的特殊情形，并通过大量模拟研究评估了最大似然估计量的有限样本性能。最后，我们将模型应用于温度数据集分析，展示了其实用价值。