Kenya has in recent years experienced a surge in extreme rainfall events, which continue to pose serious risks to human life, infrastructure, and the wider economy. This study aimed to develop a non-stationary Generalized Pareto Distribution(GPD). Its performance was compared with the classical stationary Peaks-Over-Threshold (POT) model to improve the modeling and prediction of extreme rainfall events. Accurately modeling these extremes is therefore essential to support sound risk assessment and informed decision-making. An Extreme Value Theory(EVT)–based threshold exceedance framework was used to model rainfall extremes, contrasting stationary and non-stationary Generalized Pareto formulations. Under the non-stationary framework, key environmental covariates were incorporated. These included Sea Surface Temperature (SST), Atmospheric Moisture Content (AMC), and Impervious Surface Percentage (ISP). These covariates account for ocean-driven climate variability, atmospheric moisture availability, and land-surface modifications influencing local atmospheric moisture, respectively. The findings indicate that the most suitable model was one in which the shape parameter varied with SST and the scale parameter with AMC. This model yielded lower information criterion values, reflecting a superior fit. This preference was further supported by a likelihood-ratio test, which indicated significance at p < 0.05. The model enabled the estimation of return levels and the assessment of rainfall-related risks in Kenya. By accounting for climatic and land-surface drivers, the study offers a stronger basis for risk assessment and delivers guidance for urban planning, policymaking, and strategies for disaster preparedness.
| Published in | American Journal of Mathematical and Computer Modelling (Volume 11, Issue 1) |
| DOI | 10.11648/j.ajmcm.20261101.16 |
| Page(s) | 67-80 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Extreme Rainfall, Generalized Pareto Distribution, Peaks-over-threshold, Nonstationary Models, Return Levels
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APA Style
Mbumbu, S. M., Waititu, A., Imboga, H., Mwelu, S. (2026). Modeling Extreme Rainfall Events Using Stationary and Non-stationary Peaks-Over-Threshold Frameworks in EVT. American Journal of Mathematical and Computer Modelling, 11(1), 67-80. https://doi.org/10.11648/j.ajmcm.20261101.16
ACS Style
Mbumbu, S. M.; Waititu, A.; Imboga, H.; Mwelu, S. Modeling Extreme Rainfall Events Using Stationary and Non-stationary Peaks-Over-Threshold Frameworks in EVT. Am. J. Math. Comput. Model. 2026, 11(1), 67-80. doi: 10.11648/j.ajmcm.20261101.16
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Download@article{10.11648/j.ajmcm.20261101.16,
author = {Simion Mike Mbumbu and Anthony Waititu and Herbert Imboga and Susan Mwelu},
title = {Modeling Extreme Rainfall Events Using Stationary and Non-stationary Peaks-Over-Threshold Frameworks in EVT
},
journal = {American Journal of Mathematical and Computer Modelling},
volume = {11},
number = {1},
pages = {67-80},
doi = {10.11648/j.ajmcm.20261101.16},
url = {https://doi.org/10.11648/j.ajmcm.20261101.16},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20261101.16},
abstract = {Kenya has in recent years experienced a surge in extreme rainfall events, which continue to pose serious risks to human life, infrastructure, and the wider economy. This study aimed to develop a non-stationary Generalized Pareto Distribution(GPD). Its performance was compared with the classical stationary Peaks-Over-Threshold (POT) model to improve the modeling and prediction of extreme rainfall events. Accurately modeling these extremes is therefore essential to support sound risk assessment and informed decision-making. An Extreme Value Theory(EVT)–based threshold exceedance framework was used to model rainfall extremes, contrasting stationary and non-stationary Generalized Pareto formulations. Under the non-stationary framework, key environmental covariates were incorporated. These included Sea Surface Temperature (SST), Atmospheric Moisture Content (AMC), and Impervious Surface Percentage (ISP). These covariates account for ocean-driven climate variability, atmospheric moisture availability, and land-surface modifications influencing local atmospheric moisture, respectively. The findings indicate that the most suitable model was one in which the shape parameter varied with SST and the scale parameter with AMC. This model yielded lower information criterion values, reflecting a superior fit. This preference was further supported by a likelihood-ratio test, which indicated significance at p < 0.05. The model enabled the estimation of return levels and the assessment of rainfall-related risks in Kenya. By accounting for climatic and land-surface drivers, the study offers a stronger basis for risk assessment and delivers guidance for urban planning, policymaking, and strategies for disaster preparedness.
},
year = {2026}
}
TY - JOUR T1 - Modeling Extreme Rainfall Events Using Stationary and Non-stationary Peaks-Over-Threshold Frameworks in EVT AU - Simion Mike Mbumbu AU - Anthony Waititu AU - Herbert Imboga AU - Susan Mwelu Y1 - 2026/03/18 PY - 2026 N1 - https://doi.org/10.11648/j.ajmcm.20261101.16 DO - 10.11648/j.ajmcm.20261101.16 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 67 EP - 80 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20261101.16 AB - Kenya has in recent years experienced a surge in extreme rainfall events, which continue to pose serious risks to human life, infrastructure, and the wider economy. This study aimed to develop a non-stationary Generalized Pareto Distribution(GPD). Its performance was compared with the classical stationary Peaks-Over-Threshold (POT) model to improve the modeling and prediction of extreme rainfall events. Accurately modeling these extremes is therefore essential to support sound risk assessment and informed decision-making. An Extreme Value Theory(EVT)–based threshold exceedance framework was used to model rainfall extremes, contrasting stationary and non-stationary Generalized Pareto formulations. Under the non-stationary framework, key environmental covariates were incorporated. These included Sea Surface Temperature (SST), Atmospheric Moisture Content (AMC), and Impervious Surface Percentage (ISP). These covariates account for ocean-driven climate variability, atmospheric moisture availability, and land-surface modifications influencing local atmospheric moisture, respectively. The findings indicate that the most suitable model was one in which the shape parameter varied with SST and the scale parameter with AMC. This model yielded lower information criterion values, reflecting a superior fit. This preference was further supported by a likelihood-ratio test, which indicated significance at p < 0.05. The model enabled the estimation of return levels and the assessment of rainfall-related risks in Kenya. By accounting for climatic and land-surface drivers, the study offers a stronger basis for risk assessment and delivers guidance for urban planning, policymaking, and strategies for disaster preparedness. VL - 11 IS - 1 ER -
Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya
Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya
Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya
Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya
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