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°, 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.
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BibTeX
@misc{mishra2026copulabased,
title = {{Copula-Based Bivariate Kumaraswamy-Teissier Distributions: Modeling Temperature-Rainfall Dependence and Compound Extremes}},
author = {Kamana Mishra and Tanmay Kayal and Sarita Azad},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04740},
eprint = {2609.04740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04740},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Copula-Based Bivariate Kumaraswamy-Teissier Distributions: Modeling Temperature-Rainfall Dependence and Compound Extremes
AU - Kamana Mishra
AU - Tanmay Kayal
AU - Sarita Azad
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04740
UR - https://arxiv.org/abs/2609.04740
AB - 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.
ER -