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New intelligent eliminating uncertainty from applied models of real-life problems via quantile functions, pivotal quantities and ancillary statistics to find quantum function representing adequate quantified statistical decisions: theory and applications for exponential distribution


Aeronautics and Aerospace Open Access Journal
Nicholas Nechval,1 Gundars Berzins,1 Konstantin Nechval2

Abstract

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 analytical methodology is illustrated in terms of the exponential distribution. Applications to other log-location scale distributions could follow directly.

Keywords

mathematical models, parametric uncertainty, pivotal quantities, ancillary statistics, certainty quantification, eliminating uncertainty, adequate quantified statistical decisions, numerical examples

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