Poisson perturbations
ESAIM: Probability and Statistics (2010)
- Volume: 3, page 131-150
- ISSN: 1292-8100
Access Full Article
top
Abstract
topHow to cite
topBarbour, Andrew D., and Xia, Aihua. "Poisson perturbations." ESAIM: Probability and Statistics 3 (2010): 131-150. <http://eudml.org/doc/197774>.
@article{Barbour2010,
abstract = {
Stein's method is used to prove approximations in total variation to the
distributions of integer valued random variables by (possibly signed)
compound Poisson measures. For sums of independent random variables,
the results obtained are very explicit, and improve upon earlier
work of Kruopis (1983) and Čekanavičius (1997);
coupling methods are used to derive concrete expressions for the error
bounds. An example is given to illustrate the potential for application
to sums of dependent random variables.
},
author = {Barbour, Andrew D., Xia, Aihua},
journal = {ESAIM: Probability and Statistics},
keywords = {Stein's method; signed compound Poisson measure; total variation;
coupling.; coupling; sums of random variables; compound measures},
language = {eng},
month = {3},
pages = {131-150},
publisher = {EDP Sciences},
title = {Poisson perturbations},
url = {http://eudml.org/doc/197774},
volume = {3},
year = {2010},
}
TY - JOUR
AU - Barbour, Andrew D.
AU - Xia, Aihua
TI - Poisson perturbations
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 131
EP - 150
AB -
Stein's method is used to prove approximations in total variation to the
distributions of integer valued random variables by (possibly signed)
compound Poisson measures. For sums of independent random variables,
the results obtained are very explicit, and improve upon earlier
work of Kruopis (1983) and Čekanavičius (1997);
coupling methods are used to derive concrete expressions for the error
bounds. An example is given to illustrate the potential for application
to sums of dependent random variables.
LA - eng
KW - Stein's method; signed compound Poisson measure; total variation;
coupling.; coupling; sums of random variables; compound measures
UR - http://eudml.org/doc/197774
ER -
References
top- M. Abramowitz and I.A. Stegun, Handbook of mathematical functions. Dover, New York (1964).
- R. Arratia, A.D. Barbour and S. Tavaré, The number of components in a logarithmic combinatorial structure. Ann. Appl. Probab., to appear.
- R. Arratia, L. Goldstein and L. Gordon, Poisson approximation and the Chen-Stein method. Stat. Science5 (1990) 403-434.
- A.D. Barbour and J.L. Jensen, Local and tail approximations near the Poisson limit. Scand. J. Statist.16 (1989) 75-87.
- A.D. Barbour and S. Utev, Solving the Stein equation in compound Poisson approximation. Adv. in Appl. Probab.30 (1998) 449-475.
- A.D. Barbour and S. Utev, Compound Poisson approximation in total variation. Stochastic Process. Appl., to appear.
- V. Cekanavicius, Asymptotic expansions in the exponent: A compound Poisson approach. Adv. in Appl. Probab.29 (1997) 374-387.
- P. Eichelsbacher and M. Roos, Compound Poisson approximation for dissociated random variables via Stein's method (1998) preprint.
- J. Kruopis, Precision of approximations of the generalized Binomial distribution by convolutions of Poisson measures. Lithuanian Math. J.26 (1986) 37-49.
- T. Lindvall, Lectures on the coupling method. Wiley, New York (1992).
- E.L. Presman, Approximation of binomial distributions by infinitely divisible ones. Theory. Probab. Appl.28 (1983) 393-403.
- D.A. Raikov, On the decomposition of Gauss and Poisson laws. Izv. Akad. Nauk Armyan. SSR Ser. Mat.2 (1938) 91-124.
- M. Roos, Stein-Chen method for compound Poisson approximation. Ph.D. Dissertation, University of Zürich (1993).
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.