• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.451-457
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• 2002

We derive the strong laws of large numbers for weighted averages of partial sums of random variables which are either associated or negatively associated. Our theorems extend and generalize strong law of large numbers for weighted sums of associated and negatively associated random variables of Matula(1996; Probab. Math. Statist. 16) and some results in Birkel(1989; Statist. Probab. Lett. 7) and Matula (1992; Statist. Probab. Lett. 15 ).

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.815-828
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• 2006

Let {$V_{nk},\;k\;{\geq}\;1,\;{\geq}\;1$} be an array of rowwise independent random elements which are stochastically dominated by a random variable X with $E\|X\|^{\frac{\alpha}{\gamma}+{\theta}}log^{\rho}(\|X\|)\;<\;{\infty}$ for some ${\rho}\;>\;0,\;{\alpha}\;>\;0,\;{\gamma}\;>\;0,\;{\theta}\;>\;0$ such that ${\theta}+{\alpha}/{\gamma}<2$. Let {$a_{nk},k{\geq}1,n{\geq}1$) be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form $\sum{^\infty_k_=_1}\;a_{nk}V_{nk}$.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1879-1903
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• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.477-489
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• 2016

The purpose of this paper is to establish the complete moment convergence and the integrability of supremum for weighted sums of pairwise negatively quadrant dependent random variables satisfying stochastically dominating condition.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.897-907
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• 2017

In this paper, we consider the strong stability of a type of Jamison weighted sums, which not only extend the corresponding result of Jamison etc. [13] from i.i.d. case to END random variables, but also obtain the necessary and sufficient results. As an important consequence, we present the result of SLLN as that of i.i.d. case.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1101-1111
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• 2008

Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.419-425
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• 1996

Let ${X, X_n, n \geq 1}$ be a sequence of independent and identically distributed(i.i.d) random variables with EX = 0 and $E$\mid$X$\mid$^p < \infty$ for some $p \geq 1$. Let ${a_{ni}, 1 \leq i \leq n, n \geq 1}$ be a triangular arrary of constants. The almost sure(a.s) convergence of weighted sums $\sum_{i=1}^{n} a_{ni}X_i$ can be founded in Choi and Sung[1], Chow[2], Chow and Lai[3], Li et al. [4], Stout[6], Sung[8], Teicher[9], and Thrum[10].

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.771-778
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• 2006

Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment conditions on both the weights and the distribution. The result obtained extends and sharpens the result of Sung ([12]).

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.275-282
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• 2004

Let {$a_{ni},\;u_n\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be an arry of constants. Let {X_{ni},\;u_n\;{\leq}\;i\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be {$a_{ni}$}-uniformly integrable random variables. Weak laws for the weighted sums ${{\Sigma}_{i=u_n}}^{{\upsilon}_n}\;a_{ni}X_{ni}$ are obtained.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.407-415
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• 2011

We establish strong laws of large numbers for weighted sums of arrays of negatively associated random variables under the condition of h-integrability and suitable conditions on the array of weights.