The Topp-Leone XLindley Distribution: Properties, Estimation and Applications to Lifetime Data
This study addresses the limited flexibility of existing two-parameter lifetime distribution models in characterizing complex tail behaviors by constructing a novel XLindley distribution based on the Topp-Leone family. The statistical properties of the proposed model, including moments, entropy, and reliability functions, are systematically derived, with parameters estimated via maximum likelihood. Monte Carlo simulations validate the robustness of the estimators, while empirical analysis using a bank customer waiting time dataset demonstrates that the new model achieves significantly superior fitting accuracy compared to conventional distributions. This work provides a mathematically rigorous tool with favorable tail behavior for lifetime data modeling.