Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Articles

INTEGRATED STATISTICAL MODELLING OF IRON EXCEEDANCE RISK: A MONTE CARLO, LOGISTIC REGRESSION, RANDOM FOREST, AND SOBOL ANALYSIS APPROACH

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  • Rachid El Chaal,
  • Hamid Dalhi,
  • Otmane Darbal,
  • Moulay Othman Aboutafail
Rachid El Chaal
ENSA of Kenitra, Engineering Sciences Laboratory, Data Analysis, Mathematical Modeling and Optimization Team, Ibn Tofail University, Morocco
Hamid Dalhi
ENSA of Kenitra, Engineering Sciences Laboratory, Data Analysis, Mathematical Modeling and Optimization Team, Ibn Tofail University, Morocco
Otmane Darbal
ENSA of Kenitra, Engineering Sciences Laboratory, Data Analysis, Mathematical Modeling and Optimization Team, Ibn Tofail University, Morocco
Moulay Othman Aboutafail
ENSA of Kenitra, Engineering Sciences Laboratory, Data Analysis, Mathematical Modeling and Optimization Team, Ibn Tofail University, Morocco
DOI: https://doi.org/10.30598/barekengvol20iss1pp0637-0656
Published November 24, 2025
Keywords
  • Kolmogorov-Smirnov test,
  • Log-Normal,
  • Monte Carlo simulation,
  • Sobol sensitivity analysis,
  • Statistical modelling,
  • Water quality
    • ...More
    Less
How to Cite
[1]
R. E. Chaal, H. Dalhi, O. Darbal, and M. O. Aboutafail, “INTEGRATED STATISTICAL MODELLING OF IRON EXCEEDANCE RISK: A MONTE CARLO, LOGISTIC REGRESSION, RANDOM FOREST, AND SOBOL ANALYSIS APPROACH”, BAREKENG: J. Math. & App., vol. 20, no. 1, pp. 0637-0656, Nov. 2025.

Copyright (c) 2025 Rachid El Chaal, Hamid Dalhi, Otmane Darbal, Moulay Othman Aboutafail

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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

The quality of water resources in the Inaouen watershed, northern Morocco, is increasingly threatened by metal contamination, particularly iron (Fe). This study implements an integrated statistical framework to assess the risk of exceeding regulatory iron concentration thresholds. After preprocessing local physico-chemical data, a binary indicator variable was constructed to flag exceedances of the critical 30 µg/L threshold. Iron concentrations were modeled using log-normal and Weibull distributions, with a Monte Carlo simulation (n = 10,000) based on the log-normal law estimating exceedance probabilities across multiple thresholds (30, 50, 100 µg/L), revealing an 18% risk at 30 µg/L. Predictive modeling via logistic regression and random forest analysis identified calcium (Ca) as the dominant driver of iron exceedances, a finding corroborated by Sobol sensitivity analysis (S1 index = 0.74), with bicarbonate (HCO₃⁻) emerging as a secondary factor (S1 = 0.10). These results demonstrate the power of combining distribution fitting, machine learning, and global sensitivity analysis to effectively quantify and interpret iron contamination risks in vulnerable watersheds such as Inaouen. The proposed methodology offers a robust decision-support tool for sustainable water resource management and public health protection.

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