Asymptotic Behavior of Weighted Sums of Weakly Negative Dependent Random Variables

	Asymptotic Behavior of Weighted Sums of Weakly Negative Dependent Random Variables
Journal of Sciences, Islamic Republic of Iran
مقاله 7، دوره 19، شماره 4، اسفند 2008 اصل مقاله (276.72 K)
چکیده
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

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