• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.55-63
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• 2001

In this paper, we derive a general strong law of large numbers and a general weak law of large number for normed weighted sums of pairwise negative quadrant dependent random variables with the common distribution function.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.885-893
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• 2009

In this paper we study the strong law of large numbers for weighted average of pairwise negatively quadrant dependent random variables. This result extends that of Jamison et al.(Convergence of weight averages of independent random variables Z. Wahrsch. Verw Gebiete(1965) 4 40-44) to the negative quadrant dependence.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.369-378
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• 2002

Strong laws of large numbers for weighted sums of asymptotically almost negatively associated(AANA) sequence are proved by our generalized maximal inequality for AANA random variables at a crucial step.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.91-109
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• 1995

The rate of convergence to a random variable S for an almost certainly convergent series $S_n = \sum^n_{j=1} X_j$ of independent random variables is studied in this paper. More specifically, when $S_n$ converges to S almost certainly, the tail series $T_n = \sum^{\infty}_{j=n} X_j$ is a well-defined sequence of random variable with $T_n \to 0$ a.c. Various sets of conditions are provided so that for a given numerical sequence $0 < b_n = o(1)$, the tail series strong law of large numbers $b^{-1}_n T_n \to 0$ a.c. holds. Moreover, these results are specialized to the case of the weighted i.i.d. random varialbes. Finally, example are provided and an open problem is posed.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.377-384
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• 1998

Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.411-422
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• 2017

Let {$X_{ni}$, $i{\geq}1$, $n{\geq}1$} be an array of rowwise asymptotically negatively associated random variables and {$a_{ni}$, $i{\geq}1$, $n{\geq}1$} an array of constants. Some results concerning complete convergence of weighted sums ${\sum}_{i=1}^{n}a_{ni}X_{ni}$ are obtained. They generalize some previous known results for arrays of rowwise negatively associated random variables to the asymptotically negative association case.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.145-153
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• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.57-67
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• 1997

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.827-840
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• 2009

Let {$X_{ni}$ | $1{\leq}i{\leq}n,\;n{\geq}1$} be an array of rowwise negatively dependent (ND) random variables. We in this paper discuss the conditions of ${\sum}^n_{t=1}a_{ni}X_{ni}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed setting and the strong law of large numbers for weighted sums of arrays of rowwise negatively dependent random variables is also considered.

• Geophysics and Geophysical Exploration
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• v.16 no.1
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• pp.1-5
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• 2013

Stacking in seismic processing plays an important role in improving signal-to-noise ratio and imaging quality of seismic data. However, the conventional stacking method doesn't remove random noises with various distributions and outliers up to a satisfactory level. This paper introduces a robust and optimum weighted stack method which shows both robustness to outlier noises and optimum in removing random noises. This was achieved by combining the robust median stacking with the optimum weighted stacking using local correlation. Application of the method to synthetic data showed that the proposed method is very effective in suppressing random noises with various distributions including outliers.