Approximation Results for Sums of Independent Random Variables
In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of n independent random variables under moment conditions. We use Stein’s method to derive the approximation results in total variation distance. The error bounds obtained are either comparable to or imp...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2022-07-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/378 |
| _version_ | 1817998304963723264 |
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| author | Pratima Eknath Kadu |
| author_facet | Pratima Eknath Kadu |
| author_sort | Pratima Eknath Kadu |
| collection | DOAJ |
| description |
In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of n independent random variables under moment conditions. We use Stein’s method to derive the approximation results in total variation distance. The error bounds obtained are either comparable to or improvement over the existing bounds available in the literature. Also, we give an application to the waiting time distribution of 2-runs.
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| first_indexed | 2024-04-14T02:51:06Z |
| format | Article |
| id | doaj.art-37ff4911c01b41c2adab1707e9a2c1b2 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T02:51:06Z |
| publishDate | 2022-07-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-37ff4911c01b41c2adab1707e9a2c1b22022-12-22T02:16:16ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712022-07-0120310.57805/revstat.v20i3.378Approximation Results for Sums of Independent Random VariablesPratima Eknath Kadu 0K. J. Somaiya College of Arts and Commerce In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of n independent random variables under moment conditions. We use Stein’s method to derive the approximation results in total variation distance. The error bounds obtained are either comparable to or improvement over the existing bounds available in the literature. Also, we give an application to the waiting time distribution of 2-runs. https://revstat.ine.pt/index.php/REVSTAT/article/view/378Poisson and geometric distributionperturbationsprobability generating functionStein operatorStein’s method |
| spellingShingle | Pratima Eknath Kadu Approximation Results for Sums of Independent Random Variables Revstat Statistical Journal Poisson and geometric distribution perturbations probability generating function Stein operator Stein’s method |
| title | Approximation Results for Sums of Independent Random Variables |
| title_full | Approximation Results for Sums of Independent Random Variables |
| title_fullStr | Approximation Results for Sums of Independent Random Variables |
| title_full_unstemmed | Approximation Results for Sums of Independent Random Variables |
| title_short | Approximation Results for Sums of Independent Random Variables |
| title_sort | approximation results for sums of independent random variables |
| topic | Poisson and geometric distribution perturbations probability generating function Stein operator Stein’s method |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/378 |
| work_keys_str_mv | AT pratimaeknathkadu approximationresultsforsumsofindependentrandomvariables |