CaltechAUTHORS
  A Caltech Library Service

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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220104-233119403

[img] PDF - Submitted Version
See Usage Policy.

580kB

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20220104-233119403

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)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2103.08846arXivDiscussion Paper
ORCID:
AuthorORCID
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.
Funders:
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
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

Repository Staff Only: item control page