Abstract
In this paper, a general exponential form of the underlying distribution and a general conjugate prior are used to discuss the maximum likelihood and Bayesian estimation based on an adaptive progressive censored sample. A general procedure for deriving the point and interval Bayesian prediction of the future progressive censored from the same sample as well as that from an unobserved future sample is also developed. The Weibull, Pareto, and Burr Type-XII distributions are then used as illustrative examples. Finally, two numerical examples are presented for illustrating all the inferential procedures developed here.