• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.343-352
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• 2018

We study the complete convergence for sequences of dependent random variables in Hilbert spaces. Results are obtained for negatively associated random variables and ${\phi}$-mixing random variables in Hilbert spaces.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.441-452
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• 2007

The exact distributions of X + Y, XY and X/(X + Y) are derived when X and Y are independent generalized Planck random variables.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.339-353
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• 2008

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Pearson type VII random variables.

• The Journal of Natural Sciences
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• v.17 no.1
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• pp.51-54
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• 2006

A complete convergence theorem for randomly weighted sums of random variables is obtained. No conditions are imposed on the joint distributions of the random variables.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.709-718
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• 1998

In this paper we obtain strong laws of large numbers for 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our results imply extensions of Etemadi`s strong laws of large numbers for nonnegative random variables to the 2-dimensional case.

• 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.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.207-217
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• 2019

We are presented of several basic properties for negatively superadditive dependent(NSD) random variables. By using this concept we are obtained complete convergence for maximum partial sums of rowwise NSD random variables. These results obtained in this paper generalize a corresponding ones for independent random variables and negatively associated random variables.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.394-397
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• 2004

In this paper, we consider interval number-valued random variables and fuzzy number-valued random variables and discuss Choquet integrals of them. Using these properties, we define the Choquet expected value of fuzzy number-valued random variables which is a natural generalization of the Lebesgue expected value of Lebesgue expected value of fuzzy random variables. Furthermore, we discuss some application of them.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.797-804
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• 1999

In this paper we derive the almost sure convergence of weighted sums of 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our re-sults imply and extension of Etemadi's(1983) strong laws of large numbers for weighted sums of nonnegative random variables to the 2-dimensional case.

• Nuclear Engineering and Technology
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• v.54 no.6
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• pp.2084-2093
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• 2022

Probabilistic safety assessment is widely used to quantify the risks of nuclear power plants and their uncertainties. When the lognormal distribution describes the uncertainties of basic events, the uncertainty of the top event in a fault tree is approximated with the sum of lognormal random variables after minimal cutsets are obtained, and rare-event approximation is applied. As handling complicated analytic expressions for the sum of lognormal random variables is challenging, several approximation methods, especially Monte Carlo simulation, are widely used in practice for uncertainty analysis. In this study, a theoretical approach for analyzing the sum of lognormal random variables using an efficient numerical integration method is proposed for uncertainty analysis in probability safety assessments. The change of variables from correlated random variables with a complicated region of integration to independent random variables with a unit hypercube region of integration is applied to obtain an efficient numerical integration. The theoretical advantages of the proposed method over other approximation methods are shown through a benchmark problem. The proposed method provides an accurate and efficient approach to calculate the uncertainty of the top event in probabilistic safety assessment when the uncertainties of basic events are described with lognormal random variables.