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.

This paper introduces a new parsimonious class of statistical models, called the flexible exponential-G (FEx-G) family. The primary motivation for proposing the FEx-G family lies in its structural simplicity and adaptability, as it accommodates any baseline distribution without introducing additional shape parameters, thereby avoiding unnecessary model complexity. Unlike many existing generator-based families, the FEx-G family is independent of previously established generators, making it a distinct and original contribution to distribution theory. Despite its parsimonious structure, the FEx-G family exhibits remarkable flexibility, being capable of modeling both monotone and nonmonotone failure rate functions, and therefore is suitable for analyzing a wide range of non-negative real-world data. A special case, termed the flexible exponential-Kumaraswamy (FExKw) distribution, is investigated in detail. The parameters of the FExKw model are estimated using nine different estimation methods, and extensive simulation studies are conducted to evaluate and rank their performance. The practical usefulness of the FExKw distribution is illustrated through applications to four real-life datasets from environmental science, industry, and medicine, where it demonstrates superior performance compared with several well-established competing distributions.