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Minimum Volume Confidence Sets for Two-Parameter Exponential Distributions

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  • Jin Zhang

Abstract

Under a reasonable restriction, we create the minimum volume confidence set for location and scale parameters of the exponential distribution. Compared to existing methods, none of which has a minimum-area property, the new confidence set is significantly the best (most accurate) with smallest volume, for whatever confidence level, sample size, and sample data.

Suggested Citation

  • Jin Zhang, 2018. "Minimum Volume Confidence Sets for Two-Parameter Exponential Distributions," The American Statistician, Taylor & Francis Journals, vol. 72(3), pages 213-218, July.
    • Handle: RePEc:taf:amstat:v:72:y:2018:i:3:p:213-218
    DOI: 10.1080/00031305.2016.1264315
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    References listed on IDEAS

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    1. N. Balakrishnan & A. J. Hayter & W. Liu & S. Kiatsupaibul, 2015. "Confidence Intervals for Quantiles of a Two-parameter Exponential Distribution under Progressive Type-II Censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(14), pages 3001-3010, July.
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    Cited by:

    1. Liang Wang & Huizhong Lin & Yuhlong Lio & Yogesh Mani Tripathi, 2022. "Interval Estimation of Generalized Inverted Exponential Distribution under Records Data: A Comparison Perspective," Mathematics, MDPI, vol. 10(7), pages 1-20, March.
    2. A. Asgharzadeh & S. F. Bagheri & N. A. Ibrahim & M. R. Abubakar, 2020. "Optimal confidence regions for the two-parameter exponential distribution based on records," Computational Statistics, Springer, vol. 35(1), pages 309-326, March.
    3. J. M. Lennartz & S. Bedbur & U. Kamps, 2021. "Minimum area confidence regions and their coverage probabilities for type-II censored exponential data," Statistical Papers, Springer, vol. 62(1), pages 171-191, February.
    4. Bedbur, S. & Kamps, U. & Lennartz, J.M., 2019. "On a smallest confidence region for a location–scale parameter in progressively type-II censored lifetime experiments," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.

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    1. J. M. Lennartz & S. Bedbur & U. Kamps, 2021. "Minimum area confidence regions and their coverage probabilities for type-II censored exponential data," Statistical Papers, Springer, vol. 62(1), pages 171-191, February.

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