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

Springer Science and Business Media LLC - Tập 86 - Trang 827-849 - 2023
Frédéric Ouimet1,2
1California Institute of Technology, Pasadena, USA
2Université de Montréal, Montreal, Canada

Tóm tắt

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 $$\textrm{NegativeBinomial}(r,p)$$ random variable jittered by a $$\textrm{Uniform}(0,1)$$ , 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.

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