Modeling Healthcare Data with a Novel Flexible Three-Parameter Distribution

Developing flexible lifetime distributions is essential for accurately modeling reliability and lifetime data across various scientific and engineering contexts. In this work, we introduce a new three-parameter lifetime distribution, which extends the well-known two-parameter Sarhan–Tadj–Hamilton model. We derive and discuss several of its important theoretical properties, including the reliability characteristics and moments. The parameter estimation is carried out using both maximum likelihood and Bayesian approaches, providing a comprehensive comparison of inferential techniques. To further examine the efficiency and robustness of the proposed estimators, a detailed Monte Carlo simulation study is conducted under different sample sizes and parameter settings. The practical usefulness of the distribution is illustrated through its application to three real-world datasets, namely cancer and COVID-19 data, where it demonstrates superior fit and flexibility compared to existing and nested lifetime models. These findings highlight the potential of the proposed model as a valuable addition to the toolbox of applied statisticians and reliability practitioners.