Lifetime and reliability data modelling via the new type II Topp-Leone-Burr III Poisson distribution

In this study, we develop the novel type II Topp-Leone-Burr III-Poisson distribution, a noteworthy contribution to the family of power series distributions. Motivated by the need for more versatile statistical tools, this study aims to develop a highly adaptable lifetime distribution for complex data phenomena. This model demonstrates significant flexibility in effectively modelling skewed data, making it a valuable tool for advanced statistical analysis. We derived some statistical properties of the proposed model. Furthermore, we presented four parameter estimation methods, with the maximum likelihood estimation emerging as the preferred approach due to its faster convergence. To ensure the robustness of these estimates, a Monte Carlo simulation study was conducted, which confirmed that the proposed model consistently delivers reliable parameter estimates. To showcase its practical utility, we provide two real-world examples where this model has been effectively applied.