Published March 16, 2021
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A refined continuity correction for the negative binomial distribution and asymptotics of the median
- Creators
- Ouimet, Frédéric
Abstract
In this paper, we prove a local limit theorem and a refined continuity correction for the negative binomial distribution. We present two applications of the results. First, we find the asymptotics of the median for a Negative Binomial (r,p) random variable jittered by a Uniform (0,1), which answers a problem left open in Coeurjolly & Trépanier (2020). This is used to construct a simple, robust and consistent estimator of the parameter p, when r > 0 is known. Second, we find an upper bound on the Le Cam distance between negative binomial and normal experiments.
Additional Information
F. O. is supported by a postdoctoral fellowship from the NSERC (PDF) and the FRQNT (B3X). The author of this manuscript declares no conflict of interest.Additional details
- Eprint ID
- 112696
- Resolver ID
- CaltechAUTHORS:20220104-233119403
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- B3X
- Fonds de recherche du Québec - Nature et technologies (FRQNT)
- Created
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2022-01-05Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field