The New Extended Exponentiated Burr XII distribution: Properties and applications

Modeling lifespan data with probability distributions is essential for decision-making in biomedical and health fields. This research introduces the New Extended Exponentiated Burr XII (NEEBXII) distribution, developed using a parameter induction technique to enhance flexibility in representing diverse data types across multiple domains. The methodology involves constructing the mathematical framework of the NEEBXII distribution, detailing key components such as order statistics, the quantile function, and moments. We employ three distinct methods for parameter estimation, rigorously evaluating their efficiency and robustness. Density function plots illustrate the NEEBXII distribution’s versatility, demonstrating various forms, including right- and left-skewed behaviors, while hazard rate function plots reveal both ascending and descending characteristics. To validate the practical applicability of the proposed model, we apply actuarial measures such as value-at-risk, expected shortfall, and tail variance. Empirical analysis using insurance claims and reliability datasets demonstrates that the NEEBXII distribution consistently outperforms existing alternatives, highlighting its robustness and effectiveness in real-world applications.