Copula-Based Bivariate Kumaraswamy-Teissier Distributions: Modeling Temperature-Rainfall Dependence and Compound Extremes
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Mishra, Kamana, Kayal, Tanmay, Azad, Sarita
Institution: Indian Institute of Technology Mandi
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
SDG: Climate action
Open Access status: green
OpenAlex ID: W7211866296
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