New Applications of Computational Intelligence for Constructing Predictive or Optimal Statistical Decisions under Parametric Uncertainty

• Published in: Automatic control and computer sciences 2023-10, Vol.57 (5), p.473-489
• Main Authors: Nicholas Nechval, Berzins, Gundars, Nechval, Konstantin
• Format: Article
• Language: English
• Subjects: Computer Science; Confidence intervals; Control Structures and Microprogramming; Probability distribution functions; Software; Statistical analysis; Statistical prediction; Stochastic models; Uncertainty
• ISSN: 0146-4116; 1558-108X
• DOI: 10.3103/S0146411623050085

The technique used here emphasizes pivotal quantities and ancillary statistics relevant for obtaining tolerance limits (or confidence intervals) for anticipated outcomes of applied stochastic models 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 tolerance 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 tolerance limits. Finally, we give practical numerical examples, where the proposed analytical methodology is illustrated in terms of the exponential distribution. Applications to other log-location-scale distributions could follow directly.