A note on Poisson approximation.

Deheuvels, Paul. "A note on Poisson approximation.." Trabajos de Estadística e Investigación Operativa 36.3 (1985): 101-111. <http://eudml.org/doc/40745>.

@article{Deheuvels1985,
abstract = {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)).},
author = {Deheuvels, Paul},
journal = {Trabajos de Estadística e Investigación Operativa},
keywords = {Aproximación de Poisson; Distribución binomial; Límite; Poisson approximation; total variation distance; Kolmogorov-Smirnov distance; non-identical Bernoulli distributions},
language = {eng},
number = {3},
pages = {101-111},
title = {A note on Poisson approximation.},
url = {http://eudml.org/doc/40745},
volume = {36},
year = {1985},
}

TY - JOUR
AU - Deheuvels, Paul
TI - A note on Poisson approximation.
JO - Trabajos de Estadística e Investigación Operativa
PY - 1985
VL - 36
IS - 3
SP - 101
EP - 111
AB - 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)).
LA - eng
KW - Aproximación de Poisson; Distribución binomial; Límite; Poisson approximation; total variation distance; Kolmogorov-Smirnov distance; non-identical Bernoulli distributions
UR - http://eudml.org/doc/40745
ER -