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A refined continuity correction for the negative binomial distribution and asymptotics of the median

Ouimet, Frédéric (2021) A refined continuity correction for the negative binomial distribution and asymptotics of the median. . (Unpublished)

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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)
Related URLs:
URLURL TypeDescription Paper
Ouimet, Frédéric0000-0001-7933-5265
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.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Fonds de recherche du Québec - Nature et technologies (FRQNT)B3X
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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112696
Deposited By: George Porter
Deposited On:05 Jan 2022 14:56
Last Modified:05 Jan 2022 14:56

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