MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES
In the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. Let be a double sequence of pairwise negatively dependent random variables. If for all non-negative real nu...
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| Format: | Article |
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| Language: | English |
| Published: |
University of Tehran
2002-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31721_3052bcbe85f6bd69227ddd20b226f76a.pdf |
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| Summary: | In the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. Let be a double sequence of pairwise negatively dependent random variables. If for all non-negative real numbers t and , for 1 < p < 2, then we prove that (1). In addition, it also converges to 0 in . The results can be generalized to an r-dimensional array of random variables under condition , thus, extending Choi and Sung’s result [7] of one dimensional case for negatively dependent random variables. |
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| ISSN: | 1016-1104 2345-6914 |