AI 中文总结
该研究推导了Morillas型copula变换及相关采样算法，填补方法学空白。引入稳定尾相依函数的Morillas型扭曲框架，利用其特征识别保留极值copulas的扭曲并提出凸组合，还分析了扭曲对最大吸引域极限的影响，给出相关扭曲示例。
AI 中文摘要
推导了用于Morillas型copula到copula变换以及多元分布函数相关扭曲的随机表示和采样算法，作为副产品得到了阿基米德和阿基马克斯copulas的新型采样方案。这填补了方法学空白并促进了扭曲copulas基于模拟的应用。对于稳定尾相依函数（stdfs），引入了Morillas型扭曲框架，通过域限制的Pexider方程分析表明指数小于1的单项式扭曲可保留stdfs。利用此特征识别保留极值copulas的扭曲，并提出扭曲stdfs的凸组合以增加极值相依建模的灵活性。还分析了扭曲对最大吸引域极限的影响。在非限制性正则变化假设下确定了显式极限EVC扭曲。给出了允许在扭曲后微调极值行为的绝对单调扭曲示例以及非正则变化的2 - 绝对单调扭曲示例。
英文摘要
A stochastic representation and sampling algorithm for Morillas-type copula-to-copula transformations and related distortions of multivariate distribution functions is derived, resulting as a byproduct in a novel sampling scheme for Archimedean and Archimax copulas. This closes a methodological gap and facilitates simulation-based applications of distorted copulas. For stable tail dependence functions (stdfs), a Morillas-type distortion framework is introduced, where monomial distortions with exponents below 1 are shown to preserve stdfs via a domain-restricted Pexider equation analysis. This characterization is leveraged to identify distortions preserving extreme value copulas, and convex combinations of distorted stdfs are proposed to increase flexibility in extremal dependence modeling. The impact of distortions on maximum domain of attraction limits is also analyzed. Explicit limiting EVC distortions are identified under non-restrictive regular variation assumptions. Examples of absolutely monotone distortions allowing to fine-tune the extreme value behavior after distortion, but also of non-regularly varying 2-absolutely monotone distortions are given.
