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Approximate two‐sided tolerance intervals for normal mixture distributions

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  • Shin‐Fu Tsai

Abstract

Universal and individual two‐sided tolerance intervals that take the inherent structure of normal mixture distributions into account are introduced in this paper for the purpose of monitoring the overall population and specific subpopulations. On the basis of generalised fiducial inference, a Markov chain Monte Carlo sampler is proposed to generate realisations from the generalised fiducial distributions of unknown parameters for obtaining the required tolerance intervals. Based on the simulation results, it is shown that the proposed method can maintain the empirical coverage rates sufficiently close to the nominal level. In addition, a lake acidity monitoring study is used to illustrate the proposed method.

Suggested Citation

  • Shin‐Fu Tsai, 2020. "Approximate two‐sided tolerance intervals for normal mixture distributions," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 367-382, September.
    • Handle: RePEc:bla:anzsta:v:62:y:2020:i:3:p:367-382
    DOI: 10.1111/anzs.12302
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    References listed on IDEAS

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    1. Zimmer, Zachary & Park, DoHwan & Mathew, Thomas, 2016. "Tolerance limits under normal mixtures: Application to the evaluation of nuclear power plant safety and to the assessment of circular error probable," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 304-315.
    2. Jan Hannig & Thomas C. M. Lee, 2009. "Generalized fiducial inference for wavelet regression," Biometrika, Biometrika Trust, vol. 96(4), pages 847-860.
    3. Young, Derek S., 2010. "tolerance: An R Package for Estimating Tolerance Intervals," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i05).
    4. Shin-Fu Tsai, 2019. "Comparing Coefficients Across Subpopulations in Gaussian Mixture Regression Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 610-633, December.
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    Cited by:

    1. Junjun Jiao & Ruijie Guan, 2024. "Tolerance Interval for the Mixture Normal Distribution Based on Generalized Extreme Value Theory," Mathematics, MDPI, vol. 12(7), pages 1-11, April.

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