Ouimet, Frédéric (2021) A refined continuity correction for the negative binomial distribution and asymptotics of the median. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220104-233119403
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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.
Item Type: | Report or Paper (Discussion Paper) | ||||||
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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. | ||||||
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Subject Keywords: | local limit theorem, continuity correction, quantile coupling, negative binomial distribution, Gaussian approximation, median, comparison of experiments, Le Cam distance, total variation | ||||||
Classification Code: | 2020 MSC: Primary: 62E20; Secondary: 62F12, 62F35, 62E15, 60F15, 62B15 | ||||||
Record Number: | CaltechAUTHORS:20220104-233119403 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20220104-233119403 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 112696 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | George Porter | ||||||
Deposited On: | 05 Jan 2022 14:56 | ||||||
Last Modified: | 05 Jan 2022 14:56 |
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