• 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.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.1-6
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• 2006

We consider the issue of Bayesian prediction of the unobservable random effects, And we characterize priors that ensure approximate frequentist validity of posterior quantiles of unobservable random effects. Finally we show that the probability matching criteria for prediction of unobservable random effects in one-way random ANOVA model.

• Ocean Systems Engineering
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• v.6 no.2
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• pp.161-189
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• 2016

This paper provides a practical stochastic method by which the maximum equilibrium scour depth around a vertical pile exposed to random waves plus a current on mild slopes can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Battjes and Groenendijk (2000) wave height distribution for mild slopes including the effect of breaking waves, and using the empirical formulas for the scour depth on the horizontal seabed by Sumer and Fredsøe (2002). The present approach is valid for wave-dominant flow conditions. Results for random waves alone and random wave plus currents have been presented and discussed by varying the seabed slope and water depth. An approximate method is also proposed, and comparisons are made with the present stochastic method. For random waves alone it appears that the approximate method can replace the stochastic method, whereas the stochastic method is required for random waves plus currents. Tentative approaches to related random wave-induced scour cases on mild slopes are also suggested.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.591-602
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• 2011

In this paper we establish the central limit theorem and the strong law of large numbers for linear random fields generated by identically distributed linear negative quadrant dependent random variables on $\mathbb{Z}^2$.

• East Asian mathematical journal
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• v.34 no.1
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• pp.59-67
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• 2018

We present new recurrence formulas for the raw and central moments of a compound binomial random variable. Our approach involves relating two compound binomial random variables that have parameters with a difference of 1 for the number of trials, but which have the same parameters for the success probability for each trial. As a consequence of our recursions, the raw and central moments of a binomial random variable are obtained in a recursive manner without the use of Stirling numbers.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.333-352
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• 2017

In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.1049-1061
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• 2017

The paper presents a characterization of stable random measures, giving a canonical form of their Laplace transform. Domain of attraction of stable random measures is concerned in a theorem showing that a random measure belongs to domain of attraction of any stable random measures if and only if it varies regularly at infinity.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.127-137
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• 1992

In this paper we investigate scaling limits for associated random measures satisfying some moment conditions. No stationarity is required. Our results imply an improvement of a central limit theorem of Cox and Grimmett to associated random measure and an extension to the nonstationary case of scaling limits of Burton and Waymire. Also we prove an invariance principle for associated random measures which is an extension of the Birkel's invariance principle for associated process.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.71-80
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• 2002

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.511-526
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• 2002

In this paper, we concern with SLLN for sums Of in-dependent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and strongly tight random fuzzy sets is obtained.