Bayes credibility estimation of an exponential parameter for random censoring and incomplete information

A Bayes interval estimation for an exponential parameter Θ in a model of random censoring with incomplete information is investigated. The instant of item failure is observed if it occurs before a randomly chosen inspection time and the failure was signaled; otherwise, the experiment is terminated at the instant of inspection. An explicit expression for the posterior PDF (probability distribution function) of the parameter is derived, and a normal approximation to it based on Taylor expansion near the maximum likelihood estimate is suggested. The results of an extension simulation showed that the reparametrization Θ₁=log Θ appreciably increases the accuracy of the normal approximation. Highly accurate highest posterior density intervals for Θ₁ are derived in a closed form for a normal prior for Θ₁ or, equivalently, for the lognormal prior on Θ