Header

UZH-Logo

Maintenance Infos

Approximation of sums of conditionally independent variables by the translated Poisson distribution


Röllin, A (2005). Approximation of sums of conditionally independent variables by the translated Poisson distribution. Bernoulli, 11(6):1115-1128.

Abstract

It is shown that the distribution of the sum of a Poisson random variable and an independent approximately normally distributed integer-valued random variable can be well approximated in total variation by a translated Poisson distribution, and further that a mixed translated Poisson distribution is close to a mixed translated Poisson distribution with the same random shift but fixed variance. Using these two results, a general approach is then presented for the approximation of sums of integer-valued random variables, having some conditional independence structure, by a translated Poisson distribution. We illustrate the method by means of two examples. The proofs are mainly based on Stein's method for distributional approximation.

Abstract

It is shown that the distribution of the sum of a Poisson random variable and an independent approximately normally distributed integer-valued random variable can be well approximated in total variation by a translated Poisson distribution, and further that a mixed translated Poisson distribution is close to a mixed translated Poisson distribution with the same random shift but fixed variance. Using these two results, a general approach is then presented for the approximation of sums of integer-valued random variables, having some conditional independence structure, by a translated Poisson distribution. We illustrate the method by means of two examples. The proofs are mainly based on Stein's method for distributional approximation.

Statistics

Citations

19 citations in Web of Science®
21 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

4 downloads since deposited on 29 Nov 2010
0 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Stein's method; total variation metric; translated Poisson distribution
Language:English
Date:2005
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:Bernoulli Society for Mathematical Statistics and Probability
ISSN:1350-7265
Publisher DOI:https://doi.org/10.3150/bj/1137421642
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2189083
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1102.60022

Download

Preview Icon on Download
Filetype: PDF (Verlags-PDF) - Registered users only
Size: 128kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations