@article { author = {}, title = {Asymptotic Behavior of Weighted Sums of Weakly Negative Dependent Random Variables}, journal = {Journal of Sciences, Islamic Republic of Iran}, volume = {19}, number = {4}, pages = {-}, year = {2008}, publisher = {University of Tehran}, issn = {1016-1104}, eissn = {2345-6914}, doi = {}, abstract = {Let be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let be other sequence of positive random variables independent of and for some and for all . In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy-tailed weakly negative dependent random variables, say, , , , and , respectively, where are bounded positive real numbers and N is a nonnegative integer-valued random variables, independent of and for all . In fact, for a large class of heavy-tailed distribution functions, we show that the asymptotic relations, , hold as Finally, if and also is a sequence of identical independent positive random variables, then we prove that}, keywords = {}, url = {https://jsciences.ut.ac.ir/article_31908.html}, eprint = {https://jsciences.ut.ac.ir/article_31908_b19eb0135e87b2280c54d9631241db68.pdf} }