A non-uniform bound on Poisson approximation for a sum of negative binomial random variables
This paper uses the Stein–Chen method to determine a non-uniform bound on the point metric between the distribution of a sum of independent negative binomial random variables and a Poisson distribution with mean 1 n i i i r q , where r i and pi= I - qi are parameters of each nega...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Prince of Songkla University
2017-06-01
|
| Series: | Songklanakarin Journal of Science and Technology (SJST) |
| Subjects: | |
| Online Access: | http://rdo.psu.ac.th/sjstweb/journal/39-3/39-3-10.pdf |
| _version_ | 1819086184949743616 |
|---|---|
| author | Kanint Teerapabolarn |
| author_facet | Kanint Teerapabolarn |
| author_sort | Kanint Teerapabolarn |
| collection | DOAJ |
| description | This paper uses the Stein–Chen method to determine a non-uniform bound on the point metric between the distribution
of a sum of independent negative binomial random variables and a Poisson distribution with mean
1
n
i i
i
r q
, where r
i
and pi= I - qi are parameters of each negative binomial distribution. The result gives a good Poisson approximation when all qi
are small or λ is small. |
| first_indexed | 2024-12-21T21:16:13Z |
| format | Article |
| id | doaj.art-9d9698b150ff42b6854b26ca072c7958 |
| institution | Directory Open Access Journal |
| issn | 0125-3395 |
| language | English |
| last_indexed | 2024-12-21T21:16:13Z |
| publishDate | 2017-06-01 |
| publisher | Prince of Songkla University |
| record_format | Article |
| series | Songklanakarin Journal of Science and Technology (SJST) |
| spelling | doaj.art-9d9698b150ff42b6854b26ca072c79582022-12-21T18:50:00ZengPrince of Songkla UniversitySongklanakarin Journal of Science and Technology (SJST)0125-33952017-06-0139335535810.14456/sjst-psu.2017.39A non-uniform bound on Poisson approximation for a sum of negative binomial random variablesKanint Teerapabolarn0Department of Mathematics, Faculty of Science, Burapha University, Chonburi, 20131 ThailandThis paper uses the Stein–Chen method to determine a non-uniform bound on the point metric between the distribution of a sum of independent negative binomial random variables and a Poisson distribution with mean 1 n i i i r q , where r i and pi= I - qi are parameters of each negative binomial distribution. The result gives a good Poisson approximation when all qi are small or λ is small.http://rdo.psu.ac.th/sjstweb/journal/39-3/39-3-10.pdfnegative binomial distributionnon-uniform boundpoint metricPoisson approximationStein–Chen method |
| spellingShingle | Kanint Teerapabolarn A non-uniform bound on Poisson approximation for a sum of negative binomial random variables Songklanakarin Journal of Science and Technology (SJST) negative binomial distribution non-uniform bound point metric Poisson approximation Stein–Chen method |
| title | A non-uniform bound on Poisson approximation for a sum of negative binomial random variables |
| title_full | A non-uniform bound on Poisson approximation for a sum of negative binomial random variables |
| title_fullStr | A non-uniform bound on Poisson approximation for a sum of negative binomial random variables |
| title_full_unstemmed | A non-uniform bound on Poisson approximation for a sum of negative binomial random variables |
| title_short | A non-uniform bound on Poisson approximation for a sum of negative binomial random variables |
| title_sort | non uniform bound on poisson approximation for a sum of negative binomial random variables |
| topic | negative binomial distribution non-uniform bound point metric Poisson approximation Stein–Chen method |
| url | http://rdo.psu.ac.th/sjstweb/journal/39-3/39-3-10.pdf |
| work_keys_str_mv | AT kanintteerapabolarn anonuniformboundonpoissonapproximationforasumofnegativebinomialrandomvariables AT kanintteerapabolarn nonuniformboundonpoissonapproximationforasumofnegativebinomialrandomvariables |