Adequate Mathematical Models of the Cumulative Distribution Function of Order Statistics to Construct Accurate Tolerance Limits and Confidence Intervals of the Shortest Length or Equal Tails
Author:
Nechval Nicholas1, Berzins Gundars1, Nechval Konstantin2
Affiliation:
1. BVEF Research Institute, University of Latvia, Riga LV-1586, LATVIA 2. Transport and Telecommunication Institute, Riga LV-1019, LATVIA
Abstract
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.
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
Subject
General Mathematics
Reference12 articles.
1. Nechval, N.A. and Vasermanis, E.K., Improved Decisions in Statistics, Riga: Izglitibas soli, 2004. 2. Nechval, N.A., Berzins, G., Purgailis, M., and Nechval, K.N., Improved estimation of state of stochastic systems via invariant embedding technique, WSEAS Transactions on Mathematics, Vol. 7, 2008, pp. 141–159. 3. Nechval, N.A., Nechval, K.N., Danovich V., and Liepins, T., Optimization of new-sample and within-sample prediction intervals for order statistics, in Proceedings of the 2011 World Congress in Computer Science, Computer Engineering, and Applied Computing, WORLDCOMP'11, Las Vegas Nevada, USA, CSREA Press, July 18-21, 2011, pp. 9197. 4. Nechval, N.A., Nechval, K.N., and Berzins, G., A new technique for intelligent constructing exact -content tolerance limits with expected (1 − )-confidence on future outcomes in the Weibull case using complete or Type II censored data, Automatic Control and Computer Sciences (AC&CS), Vol. 52, 2018, pp. 476–488. 5. Nechval, N.A., Berzins, G., Nechval, K.N., and Krasts, J., A new technique of intelligent constructing unbiased prediction limits on future order statistics coming from an inverse Gaussian distribution under parametric uncertainty, Automatic Control and Computer Sciences (AC&CS), Vol. 53, 2019, pp. 223– 235.
Cited by
2 articles.
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