• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.855-863
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• 1998

Some conditions on the strong law of large numbers for weighted sums of negative quadrant dependent random variables are studied. The almost sure convergence of weighted sums of negatively associated random variables is also established, and then it is utilized to obtain strong laws of large numbers for weighted averages of negatively associated random variables.

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.177-182
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• 2004

In this paper, we establish some results on almost sure convergence for sums and weighted sums of uniformly integrable fuzzy random sets taking values in the space of upper-semicontinuous fuzzy sets in $R^{p}$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.6A
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• pp.517-523
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• 2002

The closed from of sums and weighted sums of the score functions of the locally optimum rank detectors are obtained in this paper. When we consider the asymptotic performance characteristics of a detector based on rank and sign statistics, the sums and weighted sums of the score functions have to be prepared. The efficacy of a detector can be obtained from the sums and weighted sums of the score functions. Score functions based on rank statistics, as well as those based on magnitude rank and sign statistics, have also been considered, which includes most score functions presented in the literature.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.883-894
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• 2004

We discuss in this paper the strong convergence for weighted sums of negative associated (in abbreviation: NA) arrays. Meanwhile, the central limit theorem for weighted sums of NA variables and linear process based on NA variables is also considered. As corollary, we get the results on iid of Li et al. ([10]) in NA setting.

• 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.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.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.215-220
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• 2002

In this paper, we establish weak laws of large numbers for weighted sums of convex-compactly uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

• 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]).