Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables
The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/104390 |
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| author | Qunying Wu |
| author_facet | Qunying Wu |
| author_sort | Qunying Wu |
| collection | DOAJ |
| description | The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for
PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002). |
| format | Article |
| id | doaj-art-d8ce03c8f5b4492aa4c50542bfad1c2f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d8ce03c8f5b4492aa4c50542bfad1c2f2025-02-03T05:50:47ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/104390104390Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random VariablesQunying Wu0College of Science, Guilin University of Technology, Guilin 541004, ChinaThe complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002).http://dx.doi.org/10.1155/2012/104390 |
| spellingShingle | Qunying Wu Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables Journal of Applied Mathematics |
| title | Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables |
| title_full | Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables |
| title_fullStr | Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables |
| title_full_unstemmed | Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables |
| title_short | Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables |
| title_sort | sufficient and necessary conditions of complete convergence for weighted sums of pnqd random variables |
| url | http://dx.doi.org/10.1155/2012/104390 |
| work_keys_str_mv | AT qunyingwu sufficientandnecessaryconditionsofcompleteconvergenceforweightedsumsofpnqdrandomvariables |