Bayesian estimation of reliability and hazard functions for the X-Gamma distribution

Abstract
This study presents Bayesian methods for estimating the reliability and hazard functions of the one-parameter X-Gamma (X-G) distribution, using squared error and entropy loss functions, along with a point estimation approach based on the posterior mode. The main objective is to investigate the performance of these Bayesian estimators for different sample sizes and parameter values, and to identify which estimation method provides the most accurate results under various loss functions. The performance of the methods is evaluated through simulation studies at selected values of the parameter, using the integrated mean squared error (IMSE). The results show that the choice of loss function affects estimation accuracy, highlighting the properties of the X-Gamma distribution, while the model’s single-parameter structure allows straightforward implementation.