The Poisson-binomial distribution is approximated by a Poisson law with respect to a new multi-metric (difference metric) unifying a broad class of probability metrics between discrete distributions. The accompanying non-metric situation is also considered leading to moderate- and large-deviation results. Using the Charlier B expansion and Fourier arguments, sharp bounds and asymptotic relations are given.
Publié le : 1999-12-14
Classification:
Charlier B expansion,
large deviations,
moderate deviations,
Poisson approximation,
Poisson-binomial distribution,
probability metrics
@article{1143122301,
author = {Roos, Bero},
title = {Asymptotics and sharp bounds in the Poisson approximation to the Poisson-binomial distribution},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 1021-1034},
language = {en},
url = {http://dml.mathdoc.fr/item/1143122301}
}
Roos, Bero. Asymptotics and sharp bounds in the Poisson approximation to the Poisson-binomial distribution. Bernoulli, Tome 5 (1999) no. 6, pp. 1021-1034. http://gdmltest.u-ga.fr/item/1143122301/