Complete convergence and complete moment convergence for negatively associated sequences of random variables
Abstract In this paper, we study the complete convergence and complete moment convergence for negatively associated sequences of random variables with E X = 0 $\mathbb{E}X=0$ , E exp ( ln α | X | ) < ∞ $\mathbb{E}\exp(\ln^{\alpha}|X| )<\infty$ , α > 1 $\alpha>1$ . As a result, we extend...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1107-z |
| _version_ | 1818333704434483200 |
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| author | Qunying Wu Yuanying Jiang |
| author_facet | Qunying Wu Yuanying Jiang |
| author_sort | Qunying Wu |
| collection | DOAJ |
| description | Abstract In this paper, we study the complete convergence and complete moment convergence for negatively associated sequences of random variables with E X = 0 $\mathbb{E}X=0$ , E exp ( ln α | X | ) < ∞ $\mathbb{E}\exp(\ln^{\alpha}|X| )<\infty$ , α > 1 $\alpha>1$ . As a result, we extend some complete convergence and complete moment convergence theorems for independent random variables to the case of negatively associated random variables without necessarily imposing any extra conditions. Our results generalize corresponding results obtained by Gut and Stadtmüller (Stat. Probab. Lett. 81:1486-1492, 2011) and Qiu and Chen (Stat. Probab. Lett. 91:76-82, 2014). |
| first_indexed | 2024-12-13T13:55:52Z |
| format | Article |
| id | doaj.art-5895e6e947d74ae4bda6c765bdf5a06f |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T13:55:52Z |
| publishDate | 2016-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-5895e6e947d74ae4bda6c765bdf5a06f2022-12-21T23:42:55ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-06-012016111010.1186/s13660-016-1107-zComplete convergence and complete moment convergence for negatively associated sequences of random variablesQunying Wu0Yuanying Jiang1College of Science, Guilin University of TechnologyCollege of Science, Guilin University of TechnologyAbstract In this paper, we study the complete convergence and complete moment convergence for negatively associated sequences of random variables with E X = 0 $\mathbb{E}X=0$ , E exp ( ln α | X | ) < ∞ $\mathbb{E}\exp(\ln^{\alpha}|X| )<\infty$ , α > 1 $\alpha>1$ . As a result, we extend some complete convergence and complete moment convergence theorems for independent random variables to the case of negatively associated random variables without necessarily imposing any extra conditions. Our results generalize corresponding results obtained by Gut and Stadtmüller (Stat. Probab. Lett. 81:1486-1492, 2011) and Qiu and Chen (Stat. Probab. Lett. 91:76-82, 2014).http://link.springer.com/article/10.1186/s13660-016-1107-znegatively associated random variablescomplete convergencecomplete moment convergence |
| spellingShingle | Qunying Wu Yuanying Jiang Complete convergence and complete moment convergence for negatively associated sequences of random variables Journal of Inequalities and Applications negatively associated random variables complete convergence complete moment convergence |
| title | Complete convergence and complete moment convergence for negatively associated sequences of random variables |
| title_full | Complete convergence and complete moment convergence for negatively associated sequences of random variables |
| title_fullStr | Complete convergence and complete moment convergence for negatively associated sequences of random variables |
| title_full_unstemmed | Complete convergence and complete moment convergence for negatively associated sequences of random variables |
| title_short | Complete convergence and complete moment convergence for negatively associated sequences of random variables |
| title_sort | complete convergence and complete moment convergence for negatively associated sequences of random variables |
| topic | negatively associated random variables complete convergence complete moment convergence |
| url | http://link.springer.com/article/10.1186/s13660-016-1107-z |
| work_keys_str_mv | AT qunyingwu completeconvergenceandcompletemomentconvergencefornegativelyassociatedsequencesofrandomvariables AT yuanyingjiang completeconvergenceandcompletemomentconvergencefornegativelyassociatedsequencesofrandomvariables |