Parameter estimation for a two-parameter bathtub-shaped lifetime distribution

A two-parameter distribution was revisited by Chen (2000) [7]. This distribution can have a bathtub-shaped or increasing failure rate function which enables it to fit real lifetime data sets. Maximum likelihood and Bayes estimates of the two unknown parameters are discussed in this paper. It is assumed in the Bayes case that the unknown parameters have gamma priors. Explicit forms of Bayes estimators cannot be obtained. Different approximations are used to establish point estimates and two sided Bayesian probability intervals for the parameters. Monte Carlo simulations are applied to the comparison between the maximum likelihood estimates and the approximate Bayes estimates obtained under non-informative prior assumptions. Analysis of a real data set is also been presented for illustrative purposes.