We obtain in this note evaluations of the total variation distance and of the Kolmogorov-Smirnov distance between the sum of n random variables with non identical Bernoulli distributions and a Poisson distribution. Some of our results precise bounds obtained by Le Cam, Serfling, Barbour and Hall.
It is shown, among other results, that if p1 = P (X1=1), ..., pn = P (Xn=1) satisfy some appropriate conditions, such that p = 1/n Σipi → 0, np → ∞, np2 → 0, then the total variation distance between X1+...+Xn and a Poisson distribution with expectation np is p(2Πe)-1/2(1 + o(1)).
En este trabajo consideramos evaluaciones de la distancia en variación entre leyes de Poisson, binomial y de sumas variables de Bernoulli independientes.
@article{urn:eudml:doc:40745,
title = {A note on Poisson approximation.},
journal = {Trabajos de Estad\'\i stica e Investigaci\'on Operativa},
volume = {36},
year = {1985},
pages = {101-111},
zbl = {0733.60040},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40745}
}
Deheuvels, Paul. A note on Poisson approximation.. Trabajos de Estadística e Investigación Operativa, Tome 36 (1985) pp. 101-111. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40745/