Bayesian estimation of the mixture of generalized exponential distribution: a versatile lifetime model in industrial processes

Constructing a flexible parametric classes of probability distributions is most popular approach in Bayesian analysis for the last few decades. This study is planned in the same direction for two components’ mixture of generalized exponential (GE) probability distribution by considering heterogeneous population from industry. We have considered censored sample environment due to its popularity in reliability theory. In addition, we have worked out expressions for the maximum likelihood estimates along with their variances and constructed components of the information matrix. To examine the performance of these estimators, we have evaluated their properties for different sample sizes, censoring rates, proportions of the component of mixture, and a variety of loss functions (LFs). The Bayes estimates are evaluated under squared error, entropy, squared logarithmic, and precautionary LFs. Hazard rate of GE distribution graphically and numerically compared with mixture of other life-time distributions. To highlight the practical significance, we have included an illustrative application example based on a real-life data.