A new alpha power type-II Lomax distribution with applications to radiation and materials sciences

This study introduces a novel three-parameter continuous model, termed the alpha power type II Lomax (APIILx) distribution, which is constructed by integrating the alpha power type II-G (APII-G) family with the Lomax distribution. The proposed model demonstrates remarkable flexibility and is capable of capturing a wide variety of distributional shapes. Its key statistical properties are rigorously derived. The model parameters are estimated using eight frequentist estimation methods, and the performance of these estimators is evaluated through extensive Monte Carlo simulations under diverse parameter configurations and sample sizes. The simulation findings confirm the consistency and efficiency of the estimators. To identify the most effective estimation procedure for the APIILx parameters, the estimators are ranked based on both partial and overall ranking criteria. Furthermore, the practical utility of the APIILx distribution is demonstrated through applications to four real-world datasets from medical, biomedical, and engineering sciences. The APIILx model consistently outperforms several well-known competing distributions in modeling radiotherapy, biomedical, and materials science data, highlighting its strong robustness and enhanced adaptability for diverse real-world applications.