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Highest posterior mass prediction intervals for binomial and poisson distributions

Author

Listed:
  • K. Krishnamoorthy

    (University of Louisiana at Lafayette)

  • Shanshan Lv

    (University of Louisiana at Lafayette)

Abstract

The problems of constructing prediction intervals (PIs) for the binomial and Poisson distributions are considered. New highest posterior mass (HPM) PIs based on fiducial approach are proposed. Other fiducial PIs, an exact PI and approximate PIs are reviewed and compared with the HPM-PIs. Exact coverage studies and expected widths of prediction intervals show that the new prediction intervals are less conservative than other fiducial PIs and comparable with the approximate one based on the joint sampling approach for the binomial case. For the Poisson case, the HPM-PIs are better than the other PIs in terms of coverage probabilities and precision. The methods are illustrated using some practical examples.

Suggested Citation

  • K. Krishnamoorthy & Shanshan Lv, 2018. "Highest posterior mass prediction intervals for binomial and poisson distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 775-796, October.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:7:d:10.1007_s00184-018-0658-z
    DOI: 10.1007/s00184-018-0658-z
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    References listed on IDEAS

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    1. Jan Hannig & Hari Iyer & Randy C. S. Lai & Thomas C. M. Lee, 2016. "Generalized Fiducial Inference: A Review and New Results," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1346-1361, July.
    2. Wang, Hsiuying, 2008. "Coverage probability of prediction intervals for discrete random variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 17-26, September.
    3. Wang, Hsiuying, 2010. "Closed Form Prediction Intervals Applied for Disease Counts," The American Statistician, American Statistical Association, vol. 64(3), pages 250-256.
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