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Information Journal Paper

Title

ASYMPTOTIC BEHAVIOR OF WEIGHTED SUMS OF WEAKLY NEGATIVE DEPENDENT RANDOM VARIABLES

Pages

  357-363

Abstract

 Let {Xj ; j³1} be a sequence of WEAKLY NEGATIVE DEPENDENT (denoted by, WND) random variables with common distribution function F and let {qj ; j³1} be other sequence of positive random variables independent of {Xj ; j³1} and P[a£qj £b]=1 for some 0<a£b<¥ and for all j³1. 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, max1£j£nXj, Snj=1 cjXj , Snj=1 qjXj , and SNj=1 qjXj , respectively, where {cj ; 1£j£n} are n bounded positive real numbers and N is a nonnegative integer-valued random variables, independent of qi and Xi for all i³1. In fact, for a large class of HEAVY-TAILED distribution functions, we show that the asymptotic relations,P[max1£j£n qjXj>x]~P[Snj=1 qjXj>x]~Snj=1 P[qjXj>x],hold as x®¥. Finally, if E(N)<¥ and also {qj ; j³1} is a sequence of identical independent positive random variables, then we prove that P[SNj=1 qjXj>x]~E(N). P[q1X1>x], as x®¥.

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    • Cite

    APA: Copy

    RANJBAR, V., AMINI, Y.M., & BOZORGNIA, A.. (2008). ASYMPTOTIC BEHAVIOR OF WEIGHTED SUMS OF WEAKLY NEGATIVE DEPENDENT RANDOM VARIABLES. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 19(4), 357-363. SID. https://sid.ir/paper/562503/en

    Vancouver: Copy

    RANJBAR V., AMINI Y.M., BOZORGNIA A.. ASYMPTOTIC BEHAVIOR OF WEIGHTED SUMS OF WEAKLY NEGATIVE DEPENDENT RANDOM VARIABLES. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2008;19(4):357-363. Available from: https://sid.ir/paper/562503/en

    IEEE: Copy

    V. RANJBAR, Y.M. AMINI, and A. BOZORGNIA, “ASYMPTOTIC BEHAVIOR OF WEIGHTED SUMS OF WEAKLY NEGATIVE DEPENDENT RANDOM VARIABLES,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 19, no. 4, pp. 357–363, 2008, [Online]. Available: https://sid.ir/paper/562503/en

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