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January, 1989 The Total Variation Distance Between the Binomial and Poisson Distributions
J. E. Kennedy, M. P. Quine
Ann. Probab. 17(1): 396-400 (January, 1989). DOI: 10.1214/aop/1176991519


The exact total variation distances are obtained between a binomial distribution with parameters $n$ and $p$ and Poisson distributions with means $np$ and $-n \log(1 - p)$, for small values of $p$. It is shown that the latter distance is smaller for $0 < p < c_n$ and larger for $c_n < p < a'_{n0}$, where as $n \rightarrow \infty, nc_n \rightarrow 1.596 \ldots$ and $na'_{n0} \rightarrow 3.414 \ldots.$


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J. E. Kennedy. M. P. Quine. "The Total Variation Distance Between the Binomial and Poisson Distributions." Ann. Probab. 17 (1) 396 - 400, January, 1989.


Published: January, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0664.60027
MathSciNet: MR972796
Digital Object Identifier: 10.1214/aop/1176991519

Primary: 60F05
Secondary: 62E20

Keywords: binomial , Poisson , total variation distance

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 1 • January, 1989
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