# A note on Poisson approximation.

Trabajos de Estadística e Investigación Operativa (1985)

- Volume: 36, Issue: 3, page 101-111
- ISSN: 0041-0241

## Access Full Article

top## Abstract

top## How to cite

topDeheuvels, 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 -