Physical and Biomedical Applications of a Newly Extended Version of the Log-Logistic Model Using AdaptiveProgressive Censored Sampling

This study explores an advanced three-parameter generalized log-logistic (GLL) model by incorporating an innovative shape parameter into the conventional log-logistic framework, allowing for greater flexibility in modeling data with increasing, decreasing, and bathtub-shaped failure rates. The estimation challenge under adaptive progressively TypeII censored data is addressed through both classical (likelihood-based) and Bayesian inferential methods. Utilizing observed Fisher information, asymptotic confidence intervals for unknown parameters are derived, while a Markov chain in the Monte Carlo approach is employed to obtain Bayesian point estimates and the highest posterior density intervals. In Bayes’ setup, the GLL parameters are presumed to have independent gamma conjugate priors against various symmetric and asymmetric losses. To examine the accuracy of the acquired estimators, an extensive Monte Carlo simulation is used. Four real-life data sets from the physical and biomedical industries are analyzed to illustrate the feasibility of the proposed techniques in an actual-world scenario. Numerical analyses revealed that the suggested model outperforms the other five models in the literature, including the alpha-power exponential, exponentiated exponential, log-logistic, Weibull, and gamma distributions. The findings emphasize the effectiveness of the Bayesian Markov chain Monte Carlo approach over frequentist techniques, reinforcing its practical significance in reliability analysis and survival studies.OPEN ACCESS Received: 27/03/2025 Accepted: 08/05/2025 Published: 15/08/2025