AI 中文总结
本研究提出两种基于Copula的双变量Kumaraswamy-Teissier分布，用于建模气温与降水的依赖关系，经模拟和喜马拉雅地区数据验证，其拟合效果优于现有模型，可量化复合极值风险。
AI 中文摘要
本研究通过将Kumaraswamy-Teissier边际分布与Clayton和Gumbel Copula结构相结合，提出了两种用于联合建模气温与降水的新型双变量分布。为捕捉包括正相关和负相关在内的广泛依赖模式，研究纳入了旋转Copula变体（90°、180°和270°）及其对应的尾部依赖特征。模型参数采用极大似然法和边际推断函数（IFM）方法进行估计，并通过全面的蒙特卡洛模拟研究评估其有限样本性能。所提出的模型被应用于西北喜马拉雅地区的月度格点气温与降水数据，该区域具有复杂的水文气候变异性特征。对比分析表明，所提框架优于几种现有双变量模型，且能有效捕捉夏季和冬季的下尾、上尾及非对称依赖结构。基于选定的最优拟合Copula模型，推导了单变量、联合和条件重现期，以量化复合极值的风险。结果凸显了所提方法能够更真实地表征水文气候依赖关系，并为评估山区极端气温和降水事件的风险提供了稳健框架。
英文摘要
This study proposes two novel bivariate distributions for jointly modeling temperature and rainfall by integrating Kumaraswamy-Teissier marginals with Clayton and Gumbel copula structures. To capture a wide range of dependence patterns, including both positive and negative associations, rotated copula variants (90°, 180°, and 270°) are incorporated along with their corresponding tail dependence characteristics. Model parameters are estimated using maximum likelihood and the inference functions for margins (IFM) approach, and their finite-sample performance is assessed through a comprehensive Monte Carlo simulation study. The proposed models are applied to monthly gridded temperature and rainfall data from the Northwest Himalayas, a region characterized by complex hydro-climatic variability. Comparative analysis demonstrates that the proposed framework outperforms several existing bivariate models and effectively captures lower-tail, upper-tail, and asymmetric dependence structures across summer and winter seasons. Based on the selected best-fitting copula models, univariate, joint, and conditional return periods are derived to quantify the risk of compound extremes. The results highlight the capability of the proposed approach to provide a more realistic representation of hydro-climatic dependence and offer a robust framework for assessing the risk of extreme temperature and rainfall events in mountainous regions.
