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All Journal Zero : Jurnal Sains, Matematika, dan Terapan
Najib, Mohamad Khoirun
IPB University
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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Evaluation of Best-Fit Probability Distribution Models for Monthly Rainfall in the Lake Toba Region Rafhida, Syukri Arif; Nurdiati, Sri; Budiarti, Retno; Najib, Mohamad Khoirun
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i2.25688

Abstract

Understanding rainfall's statistical distribution is crucial for effective water resource management, disaster mitigation, and climate adaptation in tropical regions. This study identifies the best-fit probability distributions for monthly rainfall in the Lake Toba region, Indonesia, based on long-term data from 34 rain gauge stations. Ten commonly used probability distributions were evaluated, with parameters estimated via Maximum Likelihood Estimation (MLE). The Kolmogorov-Smirnov (KS) test was applied to assess model goodness-of-fit at each station and month. Results indicate that the Generalized Extreme Value (GEV), Gamma, and Weibull distributions consistently provide the best fit for most stations and regencies, while Exponential and Inverse Gaussian distributions perform poorly. Spatial analysis reveals notable variation in best-fit models among regencies, emphasizing the influence of local topography and microclimate. These results highlight the need to select flexible probability models for hydrological planning and climate risk assessment in complex tropical regions. The findings provide valuable references for rainfall modeling and bias correction elsewhere.
Modeling Monthly Rainfall Data Using the Alpha Power Transformed X-Lindley Distribution in the Toba Lake Region Najib, Mohamad Khoirun; Nurdiati, Sri; Khatizah, Elis; Firdawanti, Aulia Rizki; Irwandi, Hendri; Azhari, Mirza Farhan; Martal, David Vijanarco; Abisha, Nicholas
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i3.25692

Abstract

Modeling rainfall is crucial for hydrological studies and climate adaptation, especially in regions with complex topography such as the Toba Lake area, North Sumatra. Classical probability distributions often struggle to represent skewness, heavy tails, and variability observed in tropical rainfall. This study explores APTXL distribution as a flexible two-parameter model. Through the alpha power transformation, APTXL extends the X-Lindley distribution by introducing an additional shape parameter, allowing better accommodation of asymmetrical and extreme values while maintaining analytical tractability. Statistical properties are derived, and parameters are estimated using maximum likelihood. The model is applied to a long-term dataset from 13 meteorological stations, covering 408 monthly observations per station. Comparative analysis against Gamma, Lognormal, and Generalized Extreme Value distributions using multiple goodness-of-fit criteria indicates that APTXL provides consistently improved performance. These results suggest APTXL as a practical tool for rainfall modeling and water-resource applications in climate-sensitive regions.
Co-Authors Abisha, Nicholas Azhari, Mirza Farhan Budiarti, Retno Firdawanti, Aulia Rizki Irwandi, Hendri Khatizah, Elis Martal, David Vijanarco Rafhida, Syukri Arif Sri Nurdiati