Published April 11, 2023
| public
Journal Article
A refined continuity correction for the negative binomial distribution and asymptotics of the median
- Creators
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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 NegativeBinomial(r,p) random variable jittered by a Uniform(0,1), which answers a problem left open in Coeurjolly and Trépanier (Metrika 83(7):837–851, 2020). This is used to construct a simple, robust and consistent estimator of the parameter p, when r > 0 is known. The case where r is unknown is also briefly covered. Second, we find an upper bound on the Le Cam distance between negative binomial and normal experiments.
Additional Information
We thank the referee for carefully reading the manuscript and for his/her helpful comments and suggestions which led to improvements in the writing of this paper. The author was previously supported by a postdoctoral fellowship from the NSERC (PDF) and the FRQNT (B3X supplement). The author is currently supported by a postdoctoral fellowship (CRM-Simons) from the Centre de recherches mathématiques (Université de Montréal) and the Simons Foundation.Additional details
- Eprint ID
- 119877
- Resolver ID
- CaltechAUTHORS:20230307-207211000.42
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- B3X
- Fonds de recherche du Québec - Nature et technologies (FRQNT)
- Université de Montréal
- Simons Foundation
- Created
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2023-04-11Created from EPrint's datestamp field
- Updated
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2023-04-11Created from EPrint's last_modified field