Bayesian estimation of 3-component mixture geometric distribution under different loss functions

This article focuses on discrete survival data analysis, employing a doubly Type-I censoring scheme (DT1SC) under a Bayesian framework for parameters estimation in a 3-component mixture geometric (3-CMG) distribution. The non-informative (uniform) prior is utilized under squared error, DeGroot, and precautionary loss functions. The time is considered as discrete in this paper, presenting a departure from continuous approaches in survival analysis. The methodology is tailored to address challenges that traditional survival analysis encounters when faced with limited or missing information. The proposed method effectively handles the complexities arising from incomplete or missing data, providing a robust mechanism for accurate parameter estimation. Through extensive simulations and application to real-world datasets, our approach demonstrates its effectiveness in managing uncertainties, particularly in scenarios involving sparse or missing data. This work represents a noteworthy contribution to methodological advancements in survival analysis, offering a valuable tool for researchers and practitioners navigating intricate dynamics within the 3-CMG under DT1CS with time being considered as discrete.