Copula-Based Bivariate Kumaraswamy-Teissier Distributions: Modeling Temperature-Rainfall Dependence and Compound Extremes

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{\deg}, 180{\deg}, and 270{\deg}) 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.