Tolerance Limits on Order Statistics in Future Samples Coming from the Two-Parameter Exponential Distribution
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 2-1, March 2016, Pages: 1-6
Received: Sep. 9, 2015; Accepted: Sep. 10, 2015; Published: Nov. 30, 2015
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Authors
Nicholas A. Nechval, Department of Mathematics, Baltic International Academy, Riga, Latvia
Konstantin N. Nechval, Department of Applied Mathematics, Transport and Telecommunication Institute, Riga, Latvia
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Abstract
This paper presents an innovative approach to constructing lower and upper tolerance limits on order statistics in future samples. Attention is restricted to invariant families of distributions under parametric uncertainty. The approach used here emphasizes pivotal quantities relevant for obtaining tolerance factors 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 past data are complete or Type II censored. The proposed approach requires a quantile of the F distribution and is conceptually simple and easy to use. For illustration, the two-parameter exponential distribution is considered. A practical example is given.
Keywords
Order Statistics, F Distribution, Lower Tolerance Limit, Upper Tolerance Limit
To cite this article
Nicholas A. Nechval, Konstantin N. Nechval, Tolerance Limits on Order Statistics in Future Samples Coming from the Two-Parameter Exponential Distribution, American Journal of Theoretical and Applied Statistics. Special Issue: Novel Ideas for Efficient Optimization of Statistical Decisions and Predictive Inferences under Parametric Uncertainty of Underlying Models with Applications. Vol. 5, No. 2-1, 2016, pp. 1-6. doi: 10.11648/j.ajtas.s.2016050201.11
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