Bayesian and Classical Methods for Log Logistic Distribution: Exploring Upper Record Values in Bladder Cancer Remission Times

This research explores Bayesian and classical estimation methods for the Log Logistic distribution, focusing on upper record values in bladder cancer remission times. Bayesian estimates are derived under informative and non-informative priors, using independent Gamma distributions to model the shape and scale parameters. Due to the non-closed form of Bayes and Maximum Likelihood estimators, numerical techniques such as Newton–Raphson and Markov Chain Monte Carlo simulations are utilized for their computation. Sensitivity analysis, involving variations in hyperparameters, evaluates the impact of prior information on estimation outcomes. The study includes a simulation study and an analysis of real-world data from bladder cancer remission times to assess the efficacy of these numerical methods. This research contributes to advancing the understanding of statistical methods for analyzing upper record values in medical research contexts, particularly in modeling and interpreting remission times for bladder cancer patients.