Bayesian Analysis of the Discrete Two-Parameter Bathtub Hazard Distribution

A new discrete two-parameter bathtub hazard distribution is proposed by Sarhan \cite{Sarhan-2017}. This paper uses Bayes method to estimate the two unknown parameters and the reliability measures of this distribution. The joint posterior distribution of the model parameters cannot be obtained in a convenient form. Therefore, numerical techniques are  needed. We apply four Bayesian numerical methods to get random draws from the joint posterior distribution to be used to estimate the model parameters and its reliability measures without deriving the actual joint posterior distribution.  It is assumed here that the two model parameters are priori independent random variables with beta and gamma distributions. Two scenarios for the hyperparameters are applied to compare their contributions on the Bayesian inferences. Two real data sets are re-analyzed using the Bayesian techniques applied here. A simulation study is performed to investigate the properties of the methods applied.