Bayesian and Classical Inference for the Generalized Log-Logistic Distribution with Applications to Survival Data

Area of Science:

• Statistics
• Survival Analysis
• Reliability Engineering

Background:

• Traditional log-logistic distribution has limitations in modeling complex hazard rate shapes.
• Survival data often exhibit variable hazard rates requiring flexible modeling approaches.

Purpose of the Study:

• Introduce and analyze the mathematical and statistical properties of a novel generalized log-logistic distribution.
• Assess the performance of parameter estimation methods for the proposed distribution.
• Demonstrate the distribution's utility in modeling real-world survival data.

Main Methods:

• Derivation of fundamental mathematical and statistical properties.
• Parameter estimation using the maximum likelihood method.
• Monte Carlo simulation studies to evaluate estimator performance.
• Application to a real-world dataset with comparisons to existing distributions.
• Bayesian inference using Markov chain Monte Carlo (MCMC) techniques.

Main Results:

• The proposed generalized log-logistic distribution encompasses several well-known lifetime distributions as special cases.
• Simulation studies indicate good performance of the maximum likelihood estimators.
• The new distribution demonstrated superior fit and flexibility compared to Weibull, log-logistic, Burr XII, and other three-parameter distributions on real-world data.
• Goodness-of-fit, log-likelihood, and information criteria supported the plausibility of the proposed distribution.
• Bayesian estimates and credible intervals were successfully computed using MCMC methods.

Conclusions:

• The generalized log-logistic distribution provides a flexible and powerful tool for survival and reliability data analysis.
• It effectively models both monotone and nonmonotone hazard rate functions, common in various applications.
• The distribution's performance is validated through simulations and real-world data analysis, showing advantages over existing models.