International Journal of Applied Mathematics and Machine LearningAuthor's: N. A. Nechval, G. Berzins, K. N. Nechval and M. Moldovan
Pages: [43] - [81]
Received Date: December 22, 2022
Submitted by: Professor Jianqiang Gao
DOI: http://dx.doi.org/10.18642/ijamml_7100122268
The method used here focuses on the basic quantities and supporting statistics needed to construct prediction limits or optimal solutions for expected outcomes under the parametric uncertainty of applied stochastic models. It is applicable whenever the statistical problem is invariant under a group of transformations acting transitively on the parameter space. This method does not require any tabulation and is applicable whether the statistics are complete or Type II censored. The exact prediction limits of the order statistics associated with a sample of basic distributions can be found quickly and easily, making tables, simulations, Monte Carlo estimated percentiles, special computer programs, and approximations unnecessary. The proposed technique is based on the transformation of probabilities and the averaging of reference values. It is conceptually simple and easy to use. The discussion is limited to one-sided prediction limits. Finally, we provide practical numerical examples where the proposed analytical methodology is illustrated in terms of the one-parameter (or two-parameter) exponential distribution. Applications to other log-location-scale distributions can follow directly.
anticipated outcomes, parametric uncertainty, unknown (nuisance) parameters, elimination, pivotal quantities, ancillary statistics, prediction limits, tolerance limits, optimal decisions.
