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Confidence intervals, prediction intervals and tolerance intervals for negative binomial distributions

Author

Listed:
  • Bao-Anh Dang

    (University of Louisiana at Lafayette)

  • K. Krishnamoorthy

    (University of Louisiana at Lafayette)

Abstract

The problems of constructing confidence intervals (CIs) for a proportion, prediction intervals (PIs) for a future sample size in a negative binomial sampling to observe a specified number of successes and tolerance intervals (TIs) for negative binomial distributions are considered. For interval estimating the success probability, we propose CIs based on the fiducial approach and the score method, evaluate them and compare them with available CIs with respect to coverage probability and precision. We propose PIs based on the fiducial approach and joint sampling approach, and compare them with the exact and other approximate PIs. We also propose TIs on the basis of our new CIs and evaluate them with respect to coverage probability and expected width. All three statistical intervals are illustrated using two examples with real data.

Suggested Citation

  • Bao-Anh Dang & K. Krishnamoorthy, 2022. "Confidence intervals, prediction intervals and tolerance intervals for negative binomial distributions," Statistical Papers, Springer, vol. 63(3), pages 795-820, June.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:3:d:10.1007_s00362-021-01255-y
    DOI: 10.1007/s00362-021-01255-y
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    References listed on IDEAS

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    1. Mathew, Thomas & Young, Derek S., 2013. "Fiducial-based tolerance intervals for some discrete distributions," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 38-49.
    2. Shilane David & Evans Steven N & Hubbard Alan E., 2010. "Confidence Intervals for Negative Binomial Random Variables of High Dispersion," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-41, March.
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