Advanced lifetime data modeling: Extension, structural properties and an application

This study provides a comprehensive investigation of the Toppe Leone Lomax Logarithmic Distribution (TLLomLD), a newly developed probabilistic model designed to capture various data patterns. The theoretical contribution begins with a rigorous mathematical formulation of the distribution, followed by a detailed examination of its key structural properties. To enable statistical inference, a maximum likelihood estimation (MLE) procedure is utilized for estimating the model parameters. The performance of the proposed framework is further assessed through extensive simulation experiments, demonstrating both the robustness and consistency of the estimators. Finally, the practical relevance of the TLLomLD is illustrated using a real-world dataset, where it exhibits superior adaptability compared to some existing distributions in literature. Collectively, these findings underscore the theoretical depth and applied utility of the TLLomLD, highlighting its potential as a powerful analytical tool for statisticians and applied researchers working with heterogeneous datasets.