A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan data
IntroductionAdvanced 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 interactio...
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Frontiers Media S.A.
2025-06-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2025.1585707/full |
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| author | Kevin Otieno Linda Chaba Linda Chaba Evans Omondi Evans Omondi Collins Odhiambo Collins Odhiambo Bernard Omolo Bernard Omolo |
| author_facet | Kevin Otieno Linda Chaba Linda Chaba Evans Omondi Evans Omondi Collins Odhiambo Collins Odhiambo Bernard Omolo Bernard Omolo |
| author_sort | Kevin Otieno |
| collection | DOAJ |
| description | IntroductionAdvanced 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. This study aims to develop a multivariate joint distribution model for climatic variables using the Hierarchical Archimedean Copula (HAC) framework.MethodsParametric 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.ResultsThe 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.DiscussionThe 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. |
| format | Article |
| id | doaj-art-9db6fe21d05d40c0b63f99a335a56a50 |
| institution | DOAJ |
| issn | 2297-4687 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Frontiers Media S.A. |
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| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj-art-9db6fe21d05d40c0b63f99a335a56a502025-08-20T03:07:17ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872025-06-011110.3389/fams.2025.15857071585707A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan dataKevin Otieno0Linda Chaba1Linda Chaba2Evans Omondi3Evans Omondi4Collins Odhiambo5Collins Odhiambo6Bernard Omolo7Bernard Omolo8Institute of Mathematical Sciences, Strathmore University, Nairobi, KenyaInstitute of Mathematical Sciences, Strathmore University, Nairobi, KenyaDepartment of Bioengineering and Therapeutic Sciences, School of Pharmacy, University of California, San Francisco, San Francisco, CA, United StatesInstitute of Mathematical Sciences, Strathmore University, Nairobi, KenyaAfrican Population and Health Research Center, Nairobi, KenyaInstitute of Mathematical Sciences, Strathmore University, Nairobi, KenyaCollege of Medicine, Pediatrics Department, University of Illinois, Peoria, IL, United StatesInstitute of Mathematical Sciences, Strathmore University, Nairobi, KenyaDivision of Mathematics and Computer Science, University of South Carolina Upstate, Spartanburg, SC, United StatesIntroductionAdvanced 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. This study aims to develop a multivariate joint distribution model for climatic variables using the Hierarchical Archimedean Copula (HAC) framework.MethodsParametric 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.ResultsThe 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.DiscussionThe 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.https://www.frontiersin.org/articles/10.3389/fams.2025.1585707/fullHierarchical Archimedean Copulacumulative distribution functionprobability distributiongoodness-of-fit testsvine copulamultivariate dependence |
| spellingShingle | Kevin Otieno Linda Chaba Linda Chaba Evans Omondi Evans Omondi Collins Odhiambo Collins Odhiambo Bernard Omolo Bernard Omolo A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan data Frontiers in Applied Mathematics and Statistics Hierarchical Archimedean Copula cumulative distribution function probability distribution goodness-of-fit tests vine copula multivariate dependence |
| title | A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan data |
| title_full | A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan data |
| title_fullStr | A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan data |
| title_full_unstemmed | A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan data |
| title_short | A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan data |
| title_sort | hierarchical archimedean copula hac model for climatic variables an application to kenyan data |
| topic | Hierarchical Archimedean Copula cumulative distribution function probability distribution goodness-of-fit tests vine copula multivariate dependence |
| url | https://www.frontiersin.org/articles/10.3389/fams.2025.1585707/full |
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