Modeling Monthly Rainfall Data Using the Alpha Power Transformed X-Lindley Distribution in the Toba Lake Region - Mohamad Khoirun Najib; Sri Nurdiati; Elis Khatizah; Aulia Rizki Firdawanti; Hendri Irwandi; Mirza Farhan Azhari; David Vijanarco Martal; Nicholas Abisha (ZERO: Jurnal Sains, Matematika dan Terapan, 2025)
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.