发表机构
Indian Institute of Technology Mandi; Cytel Innovation Team, Cytel Pune（印度技术学院曼迪分校; Cytel 浦那创新团队）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出KTD-VARMA混合框架，用新型Kumaraswamy-Teissier分布刻画极端降雨并变换数据，结合VARMA建模时空依赖，在喜马拉雅西北部实现更优拟合与预测。
AI 中文摘要
山区降雨建模需要能够捕捉强偏态和极值的灵活统计工具。本研究提出了一种新型混合KTD-VARMA框架来应对这一挑战。该框架首先引入Kumaraswamy-Teissier分布（KTD），这是一种通过Kumaraswamy-G生成器推导出的新三参数模型，用于统计表征极端降雨。推导了其性质，并通过极大似然、极大乘积间距和贝叶斯（MCMC）方法以及可信区间和最高后验密度区间估计参数。KTD相比其子模型提供了更优的拟合。重现期分析凸显了清晰的空间对比：德拉敦经历最频繁的极值，曼迪和坎格拉表现出中等极值行为，而西姆拉和奈尼塔尔对极端月总量显示出较长的重现期。此外，KTD作为偏态降雨序列的归一化变换，KTD变换后的数据随后使用向量自回归移动平均（VARMA）模型进行建模，以捕捉时空依赖性。这种首次提出的综合方法，在季节性调整后比使用原始数据或单变量ARIMA的模型产生更准确的预测，其中VARMA实现了最低的均方根误差（RMSE）。该工作确立了KTD-VARMA框架作为极值分析和改进多站点预测的综合工具，为山区水文风险评估提供了稳健方法。
英文摘要
This study introduces the three-parameter Kumaraswamy--Teissier distribution (KTD) by applying the Kumaraswamy-G construction to the Teissier distribution. The proposed distribution provides additional shape flexibility for modelling positive-valued observations and accommodates different density and hazard-rate shapes. Several statistical properties, including moments, the moment generating function, quantile function, and order statistics, are derived. Maximum likelihood, maximum product spacing, and Bayesian methods are considered for parameter estimation, and simulation results demonstrate improving estimation accuracy with increasing sample size. A median-based regression model is further developed for the KTD, with its finite-sample performance examined through simulation. The practical utility of the proposed regression model is demonstrated through an application to monthly gridded rainfall data from the Northwest Himalayas, incorporating annual and semi-annual harmonic terms to capture seasonal variation. Its performance is assessed against Kumaraswamy and beta regression using residual-based goodness-of-fit diagnostics and likelihood-based model selection. The results demonstrate effectiveness of the proposed distribution for modelling heterogeneous and skewed positive-valued rainfall data.
