Highest posterior mass prediction intervals for binomial and poisson distributions
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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.
KeywordsCoverage probability Fiducial method Highest probability mass function Precision Predicting distribution
The authors are grateful to two reviewers and the editor for providing valuable comments and suggestions.
- Brown LD, Cai T, Das Gupta A (2001) Interval estimation for a binomial proportion (with discussion). Stat Sci 16:101–133Google Scholar
- Fisher RA (1930) Inverse probability. In: Proceedings of the Cambridge philosophical society, London, vol xxvi, pp 528–535Google Scholar
- Fisher RA (1935) The fiducial argument in statistical inference. Ann Eugen VI:91–98Google Scholar
- Montgomery DC (1996) Introduction to statistical quality control Hoboken. Wiley, New YorkGoogle Scholar