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

Frédéric Ouimet ()
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Frédéric Ouimet: California Institute of Technology

Metrika: International Journal for Theoretical and Applied Statistics, 2023, vol. 86, issue 7, No 5, 827-849

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

Keywords: Local limit theorem; Continuity correction; Quantile coupling; Negative binomial distribution; Gaussian approximation; Median; Comparison of experiments; Le Cam distance; Total variation; Primary 62E20; Secondary 62F12; 62F35; 62E15; 60F15; 62B15 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-023-00897-2

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