Bayes Credibility Estimation of an Exponential Parameter for Random Censoring & Incomplete Information

A Bayes interval estimation for an exponential parameter 0 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 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 extensive simulation showed that the reparametrization δ, = log δ appreciably increases the accuracy of the normal approximation. Highly accurate HPD-intervals for δ1 are derived in a closed form for a normal prior for δ1, or equivalently, for the lognormal prior on 0.