Leveraging Bayesian and Classical Techniques for Survival Analysis Using the Weibull-Rayleigh Distribution

This paper contributes to an extensive analysis of the Weibull-Rayleigh distribution (WRD), including Bayesian inference for randomly censored data. The WRD is a versatile model that fits various types of survival data, especially in situations including censoring, commonly found in biostatistics and engineering reliability research. The research investigates the derivation of the WRD’s probability density and cumulative distribution functions, employing maximum likelihood estimation (MLE) and Bayesian estimating techniques to accurately infer parameters. Gamma priors are utilized in Bayesian analysis, and approximate Bayesian estimates are derived by Gibbs sampling and Lindley’s approximation methods. An actual dataset that represents leukemia-free survival times for patients undergoing allogeneic bone marrow transplants is used to demonstrate the practical application of the WRD and to validate the proposed methods. The Kolmogorov-Smirnov test confirms the WRD’s superior fit compared to alternative models. This paper provides a robust framework for applying the WRD in survival analysis and highlights the efficacy of Bayesian inference in handling complex censored data structures.