Analyzing quantitative performance: Bayesian estimation of 3-component mixture geometric distributions based on Kumaraswamy prior

This research addresses the underutilization of discrete life testing models and proposes a Bayesian estimation strategy for a 3-component mixture of geometric distributions under a doubly type-I censoring scheme. Simpler models are less good at capturing how different processes work than more complex ones. This is because simpler models only show the lifetime distributions. This paper focuses on the examination of a 3-component mixture of geometric distributions from a Bayesian perspective. We conduct the analysis within a censored sampling environment, a commonly employed method in reliability theory and survival analysis. We derive expressions for Bayes estimators and Bayes risks under the Squared Error Loss Function (SELF), the Precautionary Loss Function (PLF), and the DeGroot Loss Function (DLF) using the Kumaraswamy prior. The process includes the elicitation of hyperparameters for the Kumaraswamy prior. Notably, the study recommends the use of the SELF for optimal estimation parameters of the 3-component mixture of geometric distributions under the doubly type-I censoring scheme. This exploration contributes to advancing the application of the Bayesian approach in discrete life testing, providing valuable insights for researchers and practitioners in the field. To numerically assess the performance of Bayes estimators employing Kumaraswamy prior under different loss functions, we conducted simulations to investigate their statistical properties. This analysis involved different sample sizes and test termination times. Furthermore, to underscore the practical relevance of our findings, we present an illustrative example based on real-life data.