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All Journal Zero : Jurnal Sains, Matematika, dan Terapan
Irwandi, Hendri
National Research and Innovation Agency
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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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 Firdawanti, Aulia Rizki Khatizah, Elis Martal, David Vijanarco Najib, Mohamad Khoirun Sri Nurdiati