The flexible Lomax-G family with estimation methods and applications in hydrology and biomedicine

In this article, we introduce and investigate a new family of continuous distributions, termed the new Lomax-G (NLx-G) family, constructed via a novel generator. Several mathematical properties are derived, including quantile functions, mixture representations, and moments, together with different estimation methods. A notable special case, the NLx-exponential (NLxEx) distribution, is emphasized for its flexibility in modeling diverse data behaviors. The performance of the proposed model is examined through a comprehensive convergence analysis of estimators and supported by an extensive simulation study, which indicates that the maximum likelihood estimator performs best. To demonstrate practical utility, the NLxEx distribution is applied to three real-world datasets from hydrology, biomedical sciences, and insurance. In addition to standard goodness-of-fit measures, fitting plots are provided as further diagnostics. Across all applications and in comparison with several competing exponential-type models, the NLxEx distribution consistently yields the best fit, confirming its robustness and adaptability.