ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Statistics and Probability
Volume 11 - 2025 | doi: 10.3389/fams.2025.1585707
A Hierarchical Archimedean Copula (HAC) model for climatic variables: An application to Kenyan data
Provisionally accepted
Kevin Omondi Otieno1*
Linda Akoth Chaba1,2
Evans Omondi, Ph.D.1,3
Collins Ojwach Odhiambo1,4
Bernard Omolo1,5- 1Strathmore University, Nairobi, Kenya
- 2Department of Bioengineering and Therapeutic Sciences, School of Pharmacy, University of California, San Francisco, San Francisco, California, United States
- 3African Population and Health Research Center (APHRC), Nairobi, Kenya
- 4College of Medicine, University of Illinois at Chicago, Chicago, Illinois, United States
- 5University of South Carolina Upstate, Spartanburg, South Carolina, United States
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Background: Advanced statistical modeling techniques, such as copula-based methods, have significantly improved the forecasting of weather variables by capturing dependencies between them. However, conventional copula approaches, such as the bivariate copula, often fail to capture complex interactions in high-dimensional climate data.Objective: This study aims to develop a multivariate joint distribution model for climatic variables using the Hierarchical Archimedean Copula (HAC) framework.Methods: Parametric methods were used to fit marginal distributions to the six variables. The uniform variates were extracted using the inverse transformation technique. The structure and parameter estimation of HAC models were determined using the Recursive Maximum likelihood (RML) method. Model selection methods, Goodness of Fit (GOF) approaches, and graphical assessment were used to select the optimal HAC model.The Weibull distribution was identified as the best fit for temperature, humidity, solar energy, and cloud cover, while the Gamma distribution was most suitable for wind, and the logistic distribution for sea-level pressure. For high-dimensional data, the HAC Frank copula demonstrated computational efficiency and effectively captured dependencies among variables.The HAC-Frank model offers a reliable and computationally efficient alternative for modeling high-dimensional climate dependencies, thereby providing a robust framework for climate forecasting, risk assessment, and environmental modeling.
Keywords: Hierarchical Archimedean copula, Cumulative distribution function, Probability distribution, Goodness-of-fit tests, Vine copula, Multivariate dependence, Climate forecasting
Received: 01 Mar 2025; Accepted: 07 May 2025.
Copyright: © 2025 Otieno, Chaba, Omondi, Ph.D., Odhiambo and Omolo. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Kevin Omondi Otieno, Strathmore University, Nairobi, Kenya
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