Extending the Quasi-XLindley distribution: a new model for improved flexibility in lifetime data modeling

Abstract This work introduces the Transmuted Quasi-XLindley distribution, a novel and flexible generalization of the Quasi-XLindley model, developed through the Quadratic Rank Transmutation Map (QRTM). The distribution’s core characteristics are established through the derivation of its probability density and cumulative distribution functions, alongside various reliability functions. A comprehensive theoretical exploration is presented, covering statistical properties such as moments, moment-generating and characteristic functions, cumulant expressions, and order statistics. Additionally, the study incorporates entropy-based measures–including Renyi and Tsallis entropies–and evaluates inequality indices based on Lorenz and Bonferroni curves. Parameters are estimated via the maximum likelihood method, and the estimator’s performance is rigorously assessed using Monte Carlo simulations across different sample sizes, focusing on bias, variance, mean squared error, and standard error. The practical effectiveness and adaptability of the proposed model are demonstrated through real-world data applications, where it exhibits a superior fit compared to several well-known models.