Nonparametric Bayesian predictive distributions for future order statistics

We derive the predictive distribution for a specified order statistic, determined from a future random sample, under a Dirichlet process prior. Two variants of the approach are treated and some limiting cases studied. A practical application to monitoring the strength of lumber is discussed, including choices of prior expectation, and comparisons made to a Bayesian parametric approach. (C) 1999 Published by Elsevier Science B.V. All rights reserved.