A Novel Alpha Power-Transformed Three-Parameter Flexible Distribution (APT3-FD): Enhanced Modeling of Complex and Tail Behavior Data with Interdisciplinary Applications

This paper introduces a novel extension of the traditional alpha power-transformation method, aiming to enhance modelling flexibility for datasets exhibiting skewness, asymmetry, and complex patterns prevalent in various fields such as economics, finance, and environmental science. Existing distributions and transformation-based models have proven valuable in specific scenarios; however, they often lack independent control over skewness and tail heaviness. To address these limitations, we propose the Alpha Power-Transformed Three-Parameter Flexible Distribution (APT3-FD) as a more versatile modelling approach. The proposed model, characterized by location, scale, and shape parameters along with separate control over skewness, enables precise adjustments for asymmetrical and tail behavior, accommodating moderate to extreme tail data. To investigate the impact of different parameter configurations, tail and skewness properties as well as sample sizes on the performance of parameter estimation methods, a Monte Carlo simulation study is conducted. Also, actuarial risk measures are calculated to showcase the model as an effective estimator in real-world risk management. This study further demonstrates the versatility and robustness of APT3-FD over many different interdisciplinary studies faced with complex data features, thus expanding its application domains. DOI : https://doi.org/10.52783/pst.1858