A Lower-Bounded Extreme Value Distribution for Flood Frequency Analysis with Applications

Fatimah E. Almuhayfith (), Maher Kachour, Amira F. Daghestani, Zahid Ur Rehman, Tassaddaq Hussain and Hassan S. Bakouch ()
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Fatimah E. Almuhayfith: Department of Mathematics and Statistics, College of Science, King Faisal University, Alahsa 31982, Saudi Arabia
Maher Kachour: Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait
Amira F. Daghestani: Department of Mathematics, College of Science and Humanities, Imam Abdulrahman Bin Faisal University, Jubail 35811, Saudi Arabia
Zahid Ur Rehman: Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, Pakistan
Tassaddaq Hussain: Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, Pakistan
Hassan S. Bakouch: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Mathematics, 2025, vol. 13, issue 21, 1-24

Abstract: This paper proposes the lower-bounded Fréchet–log-logistic distribution (LFLD), a probability model designed for robust flood frequency analysis (FFA). The LFLD addresses key limitations of traditional distributions (e.g., generalized extreme value (GEV) and log-Pearson Type III (LP3)) by combining bounded support ( α < x < ∞ ) to reflect physical flood thresholds, flexible tail behavior via Fréchet–log-logistic fusion for extreme-value accuracy, and maximum entropy characterization, ensuring optimal parameter estimation. Thus, we obtain the LFLD’s main statistical properties (PDF, CDF, and hazard rate), prove its asymptotic convergence to Fréchet distributions, and validate its superiority through simulation studies showing MLE consistency (bias < 0.02 and mean squared error < 0.0004 for α ) and empirical flood data tests (52- and 98-year AMS series), where the LFLD outperforms 10 competitors (AIC reductions of 15–40%; Vuong test p < 0.01). The LFLD’s closed-form quantile function enables efficient return period estimation, critical for infrastructure planning. Results demonstrate its applicability to heavy-tailed, bounded hydrological data, offering a 20–30% improvement in flood magnitude prediction over LP3/GEV models.

Keywords: flood frequency analysis; bounded distributions; Fréchet distribution; log-logistic model; entropy; extreme value theory; return period estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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