The estimation of two-parameter exponential distribution using Bayes approach need a prior distribution for the two parameters. It is difficult to know this joint prior distribution, so it requires sometimes the approximation or to some assumptions which depends on previous experience. An estimation method was proposed by using linear transformation of reliability function of two-parameter exponential distribution in order to get simple linear regression model. Its parameters can be estimated by using Bayes approach, and then get the estimated parameters of the distribution from the relationship between the distribution parameters and regression model parameters. Simulation experiments at different sample sizes were applied in order to make a comparison between Bayes estimators yield from approximation method and estimators from proposed method. The findings show that the proposed method estimators were more efficient that from approximation method estimators by using mean squares error (MSE) as a criterion for comparison. Also, the results of estimation methods were applied on actual data taken from Babil Tires Factory, where the data represents the working time (hours) between successive failures.
Al-Ani et al. (2020) studied this question.