Intelligent Computational Approach to Constructing Adequate Statistical Decisions under Parametric Uncertainty of Applied Stochastic Models

The technique used here emphasizes pivotal quantities and ancillary statistics relevant for optimization or obtaining prediction limits (or intervals) for anticipated outcomes under parametric uncertainty 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 experimental data are complete or Type II censored. The exact prediction limits on order statistics associated with sampling from underlying distributions can be found easily and quickly making tables, simulation, Monte-Carlo estimated percentiles, special computer programs, and approximation unnecessary. The proposed technique is based on a probability transformation and pivotal quantity averaging. It is conceptually simple and easy to use. The discussion is restricted to one-sided prediction limits. Finally, we give practical numerical examples, where the proposed analytical methodology is illustrated in terms of the one-parameter exponential distribution. Applications to other log-location-scale distributions could follow directly.