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

Bao-Anh Dang and K. Krishnamoorthy ()
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Bao-Anh Dang: University of Louisiana at Lafayette
K. Krishnamoorthy: University of Louisiana at Lafayette

Statistical Papers, 2022, vol. 63, issue 3, No 4, 795-820

Abstract: 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.

Keywords: Beta-negative binomial; Coverage probability; Equal-tailed tolerance interval; Fiducial approach; Highest probability mass function; Inverse sampling; Precision (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00362-021-01255-y

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