ABSTRACT
In this paper, we consider the problems of constructing simultaneous prediction limits on future outcomes of all of l future samples using the results of a previous sample from the same underlying distribution belonging to invariant family. The prediction limits obtained in the paper are generalizations of the usual prediction limits on observations or functions of observations of only one future sample. Attention is restricted to invariant families of distributions under parametric uncertainty. The approach used here emphasizes pivotal quantities relevant for obtaining ancillary statistics and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. It does not require the construction of any tables and is applicable whether the data are complete or Type II censored. The proposed approach requires a quantile of the F distribution and is conceptually simple and easy to use. The simultaneous prediction limits on future outcomes are found and illustrated using a numerical example.
