A length-biased Sujit distribution framework: properties, simulation-based inference, and application to clinical remission data

Statistical methodologies play a crucial role in biomedical research, particularly in the analysis of clinical and survival data. In oncology, specialized statistical frameworks are often necessary to accurately characterize time-to-event outcomes. This study introduces a generalized model that yields a weighted probability distribution, specifically the Length-Biased Sujit (LBSJT) distribution, derived as an extension of the conventional Sujit model. The proposed distribution incorporates a length-biased mechanism, enhancing its flexibility for modeling survival times. A comparative analysis is conducted between the original and the length-biased versions to evaluate their respective fitting capabilities. Key theoretical properties of the LBSJT distribution are established, including raw moments, the moment generating function, and reliability-related measures. Additional analytical features such as the Bonferroni and Lorenz curves and incomplete moments are also derived. Parameter estimation is performed using the maximum likelihood approach, and a comprehensive Monte Carlo simulation is carried out to assess the precision and robustness of the estimators. The results demonstrate strong estimation accuracy, particularly with increasing sample size and parameter values. Finally, the applicability and effectiveness of the proposed distribution are demonstrated through its application to clinical remission data, where the LBSJT model provides a superior fit compared to several well-established distributions.