The Total Variation Distance Between the Binomial and Poisson Distributions
Kennedy, J. E. ; Quine, M. P.
Ann. Probab., Tome 17 (1989) no. 4, p. 396-400 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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 $na'_{n0} \rightarrow 3.414 \ldots.$
Publié le : 1989-01-14
Classification:  Total variation distance,  binomial,  Poisson,  60F05,  62E20 
@article{1176991519,
     author = {Kennedy, J. E. and Quine, M. P.},
     title = {The Total Variation Distance Between the Binomial and Poisson Distributions},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 396-400},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991519}
}

Kennedy, J. E.; Quine, M. P. The Total Variation Distance Between the Binomial and Poisson Distributions. Ann. Probab., Tome 17 (1989) no. 4, pp.  396-400. http://gdmltest.u-ga.fr/item/1176991519/