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 |
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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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| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-dc0d3f4f32474c04b17788bfbbf7aba9 |
| institution | OA Journals |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2002-09-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-dc0d3f4f32474c04b17788bfbbf7aba92025-08-20T01:53:33ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142002-09-0113331721MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLESIn 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.https://jsciences.ut.ac.ir/article_31721_3052bcbe85f6bd69227ddd20b226f76a.pdf |
| spellingShingle | MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES Journal of Sciences, Islamic Republic of Iran |
| title | MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES |
| title_full | MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES |
| title_fullStr | MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES |
| title_full_unstemmed | MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES |
| title_short | MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES |
| title_sort | marcinkiewicz type strong law of large numbers for double arrays of negatively dependent random variables |
| url | https://jsciences.ut.ac.ir/article_31721_3052bcbe85f6bd69227ddd20b226f76a.pdf |