In this paper, we introduce the Burr-X Marshall–Olkin-F (BXMO-F) family, which proves to be highly effective for real-life data analysis. We establish several of its mathematical properties and demonstrate that the BXMO-F family can accommodate a variety of hazard rates and density functions. We derive six risk measures for the BXMO-Lomax distribution, which are crucial for portfolio optimization. The parameters of the BXMO-Lomax distribution are estimated using eight different estimation approaches, and these approaches are thoroughly evaluated through detailed numerical simulations. Finally, we explore the applicability of the BXMO-Lomax distribution by analyzing two real-life data sets from engineering and medicine. Our analysis shows that the BXMO-Lomax distribution offers a superior fit compared to several well-known extensions of the Lomax distribution. |
