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Two-sided tolerance intervals in the exponential case: Corrigenda and generalizations

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  • Fernández, Arturo J.

Abstract

Exact two-sided guaranteed-coverage tolerance intervals for the exponential distribution which satisfy the traditional "equal-tailedness" condition are derived in the failure-censoring case. The available empirical information is provided by the first r ordered observations in a sample of size n. A Bayesian approach for the construction of equal-tailed tolerance intervals is also proposed. The degree of accuracy of a given tolerance interval is quantified. Moreover, the number of failures needed to achieve the desired accuracy level is predetermined. The Bayesian perspective is shown to be superior to the frequentist viewpoint in terms of accuracy. Extensions to other statistical models are presented, including the Weibull distribution with unknown scale parameter. An alternative tolerance interval which coincides with an outer confidence interval for an equal-tailed quantile interval is also examined. Several important computational issues are discussed. Three censored data sets are considered to illustrate the results developed.

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  • Fernández, Arturo J., 2010. "Two-sided tolerance intervals in the exponential case: Corrigenda and generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 151-162, January.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:1:p:151-162
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    References listed on IDEAS

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    1. D. T. Shirke & R. R. Kumbhar & D. Kundu, 2005. "Tolerance intervals for exponentiated scale family of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1067-1074.
    2. Hu, Xiaomi, 2007. "Asymptotical distributions, parameters and coverage probabilities of tolerance limits," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4753-4760, May.
    3. Ping Sa & Luminita Razaila, 2004. "One-sided Continuous Tolerance Limits and their Accompanying Sample Size Problem," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(4), pages 419-434.
    4. Fernández, Arturo J., 2008. "Reliability inference and sample-size determination under double censoring for some two-parameter models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3426-3440, March.
    5. Lin, Tsai-Yu & Liao, Chen-Tuo, 2006. "A [beta]-expectation tolerance interval for general balanced mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 911-925, February.
    6. Arturo Fernández, 2009. "Weibull inference using trimmed samples and prior information," Statistical Papers, Springer, vol. 50(1), pages 119-136, January.
    7. Gebizlioglu, Omer L. & Yagci, Banu, 2008. "Tolerance intervals for quantiles of bivariate risks and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1022-1027, June.
    8. Chen, Shun-Yi & Harris, Bernard, 2006. "On Lower Tolerance Limits With Accurate Coverage Probabilities for the Normal Random Effects Model," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1039-1049, September.
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    Cited by:

    1. Kyung Serk Cho & Hon Keung Tony Ng, 2021. "Tolerance intervals in statistical software and robustness under model misspecification," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-49, December.
    2. Fernández, Arturo J. & Pérez-González, Carlos J. & Aslam, Muhammad & Jun, Chi-Hyuck, 2011. "Design of progressively censored group sampling plans for Weibull distributions: An optimization problem," European Journal of Operational Research, Elsevier, vol. 211(3), pages 525-532, June.
    3. Fernández, Arturo J., 2012. "Minimizing the area of a Pareto confidence region," European Journal of Operational Research, Elsevier, vol. 221(1), pages 205-212.

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