THE ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LINEAR NEGATIVELY DEPENDENT RANDOM VARIABLES

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NILI SANI H.R.; AMINI M.; BOZORGNIA A.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Journal: Journal of Sciences, Islamic Republic of Iran Year:2009 | Volume:20 | Issue:1 Page(s): 67-72

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Information Journal Paper

Title

THE ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LINEAR NEGATIVELY DEPENDENT RANDOM VARIABLES

Author(s)

NILI SANI H.R. | AMINI M. | BOZORGNIA A. | Issue Writer Certificate

Keywords

PAIRWISE NEGATIVELY DEENDENTQ3

LINEAR NEGATIVELY DEPENDENTQ3

NEGATIVE ASSOCIATIONQ3

COMPLETE CONVERGENCEQ3

Abstract

In this paper, we generalize a theorem of Shao [12] by assuming that {Xn} is a sequence of LINEAR NEGATIVELY DEPENDENT random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for LINEAR NEGATIVELY DEPENDENT identically random variables with finite p –th absolute moment (p³2) p the weighted sums 1/An åni=1 aniXi converge to zero as where An=n1/p and (åni=1 a2ni) {an,i} a is an array of real numbers. Moreover, we prove the almost sure convergence for weighted sums åni=1 aniX, n³1, when {Xi, i ³ 1} i is a sequence of pairwise negative quadrant dependence stochastically bounded random variables under some suitable conditions on an,i.

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APA: Copy

NILI SANI, H.R., AMINI, M., & BOZORGNIA, A.. (2009). THE ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LINEAR NEGATIVELY DEPENDENT RANDOM VARIABLES. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 20(1), 67-72. SID. https://sid.ir/paper/84183/en

Vancouver: Copy

NILI SANI H.R., AMINI M., BOZORGNIA A.. THE ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LINEAR NEGATIVELY DEPENDENT RANDOM VARIABLES. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2009;20(1):67-72. Available from: https://sid.ir/paper/84183/en

IEEE: Copy

H.R. NILI SANI, M. AMINI, and A. BOZORGNIA, “THE ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LINEAR NEGATIVELY DEPENDENT RANDOM VARIABLES,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 20, no. 1, pp. 67–72, 2009, [Online]. Available: https://sid.ir/paper/84183/en

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