# Poisson perturbations

ESAIM: Probability and Statistics (1999)

- Volume: 3, page 131-150
- ISSN: 1292-8100

## Access Full Article

top## How to cite

topBarbour, Andrew D., and Xia, Aihua. "Poisson perturbations." ESAIM: Probability and Statistics 3 (1999): 131-150. <http://eudml.org/doc/104253>.

@article{Barbour1999,

author = {Barbour, Andrew D., Xia, Aihua},

journal = {ESAIM: Probability and Statistics},

keywords = {Stein's method; signed compound Poisson measure; total variation; coupling; sums of random variables; compound measures},

language = {eng},

pages = {131-150},

publisher = {EDP Sciences},

title = {Poisson perturbations},

url = {http://eudml.org/doc/104253},

volume = {3},

year = {1999},

}

TY - JOUR

AU - Barbour, Andrew D.

AU - Xia, Aihua

TI - Poisson perturbations

JO - ESAIM: Probability and Statistics

PY - 1999

PB - EDP Sciences

VL - 3

SP - 131

EP - 150

LA - eng

KW - Stein's method; signed compound Poisson measure; total variation; coupling; sums of random variables; compound measures

UR - http://eudml.org/doc/104253

ER -

## References

top- [1] M. Abramowitz and I.A. Stegun, Handbook of mathematical functions. Dover, New York ( 1964).
- [2] R. Arratia, A.D. Barbour and S. Tavaré, The number of components in a logarithmic combinatorial structure. Ann. Appl. Probab., to appear. Zbl1056.60012MR1768242
- [3] R. Arratia, L. Goldstein and L. Gordon, Poisson approximation and the Chen-Stein method. Stat. Science 5 ( 1990) 403-434. Zbl0955.62542MR1092983
- [4] A.D. Barbour and J.L. Jensen, Local and tail approximations near the Poisson limit. Scand. J. Statist. 16 ( 1989) 75-87. Zbl0674.60022MR1003970
- [5] A.D. Barbour and S. Utev, Solving the Stein equation in compound Poisson approximationAdv. in Appl. Probab. 30 ( 1998) 449-475. Zbl0982.62007MR1642848
- [6] A.D. Barbour and S. Utev, Compound Poisson approximation in total variation. Stochastic Process. Appl., to appear. Zbl0991.62008MR1695071
- [7] V. Čekanavičius, Asymptotic expansions in the exponent: A compound Poisson approach. Adv. in Appl. Probab. 29 ( 1997) 374-387. Zbl0895.60029MR1450935
- [8] P. Eichelsbacher and M. Roos, Compound Poisson approximation for dissociated random variables via Stein's method ( 1998) preprint. Zbl0982.62008MR1723647
- [9] J. Kruopis, Precision of approximations of the generalized Binomial distribution by convolutions of Poisson measures. Lithuanian Math. J. 26 ( 1986) 37-49. Zbl0631.60019
- [10] T. Lindvall, Lectures on the coupling method. Wiley, New York ( 1992). Zbl0850.60019MR1180522
- [11] E.L. Presman, Approximation of binomial distributions by infinitely divisible ones. Theory. Probab. Appl. 28 ( 1983) 393-403. Zbl0533.60018MR700218
- [12] D.A. Raikov, On the decomposition of Gauss and Poisson laws. Izv. Akad. Nauk Armyan. SSR Ser. Mat. 2 ( 1938) 91-124. Zbl0018.41204
- [13] M. Roos, Stein-Chen method for compound Poisson approximation. Ph. D. Dissertation, University of Zürich ( 1993). Zbl0853.60020

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.