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This study developed a new family of distributions, the Marshall-Olkin generalized distribution. A novel model, the Marshall-Olkin Lomax (NMOL) distribution, was introduced into this family. The NMOL distribution exhibited a variety of density forms, including symmetry, right-skewness, reversed-J shape, upside-down bathtub curves, and scenarios with growing, decreasing, and mixed trends. From a practical perspective, the NMOL model was used to assess the failure and insurance data. Furthermore, a group-acceptance sampling plan (GASP) was developed based on the NMOL distribution, with the median serving as a quality criterion. This analysis also included numerical and graphical representations of the expected shortfalls and values at risk. Simulation studies were conducted to evaluate the effectiveness of the proposed estimation methods, and the findings significantly validated the NMOL model. However, this new distribution family and model has wide-ranging applications in sectors such as engineering, survival analysis, hydrology, and economics.
Ameeq et al. (Sun,) studied this question.