• 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.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.19-27
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• 2001

In this paper we study another kind of the large deviation property, i.e. moderate deviation type for random amount of random measures on $R^d$ about a Poisson point process and a Poisson center cluster random measure.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.4
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• pp.307-310
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• 2001

A measure of typicality associated with any fuzzy subset on a probability space is introduced. We will improve some results of Yager and consider limit of the measure of typicality of a fuzzy set with ,respect to a random sample.

• 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.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.515-524
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• 2017

In this study, a measure of discrepancy based on MV (margin of victory) has been suggested that might be useful in determining the size of random forest for classification. Here MV is a scaled difference in the votes, at infinite random forest, of two most popular classes of current random forest. More specifically, max(-MV,0) is proposed as a reasonable measure of discrepancy by noting that negative MV values mean a discrepancy in two most popular classes between the current and infinite random forests. We propose an appropriate diagnostic statistic based on this measure that might be useful for the determination of random forest size, and then we derive its asymptotic distribution. Finally, a simulation study has been conducted to compare the performances, in finite samples, between this proposed statistic and other recently proposed diagnostic statistics.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.269-289
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• 2005

An infinite system of stochastic differential equations (SDE)driven by Brownian motions and compensated Poisson random measures for the locations and weights of a collection of particles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted measure V, which is shown to be a solution of a stochastic differential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.

• Journal of applied mathematics & informatics
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• v.3 no.1
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• pp.89-100
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• 1996

In this paper we investigate a limit theorem for a non-statioary d-parameter array of associated random variables applying the criterion of the tightness condition in Donsker, M[1951]. Our re-sults imply an extension to the nonstatioary case of Convergence of Probability Measure of billingsley. P[1986]. and analogous results for the d-dimensional associated random measure. These results are also applied to show a new limit theorem for Poisson cluster random mea-sures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.9 s.180
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• pp.2283-2291
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• 2000

The neural network method is applied to automatically measure the crack opening load under random loading. The crack opening results obtained are compared with the visual measured results. Fatigue crack growth under random loading is predicted using the crack opening data measured by the neural network method, and the prediction results are compared with experimental ones. It is found that the neural network method can be successfully applied to consistently measure the crack opening load under random loading and also gives some results different from the results by visual measurement.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.121-130
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• 2002

In this paper we prove a functional central limit theorem for a field $\{X_{\underline{j}}:{\underline{j}}{\in}Z_+^d\}$ of nonstationary associated random variables with $EX{\underline{j}}=0,\;E{\mid}X_{\underline{j}}{\mid}^{r+{\delta}}<{\infty}$ for some $r>2,\;{\delta}>0$and $u(n)=O(n^{-{\nu}})$ for some ${\nu}>0$, where $u(n):=sup_{{\underline{i}}{\in}Z_+^d{\underline{j}}:{\mid}{\underline{j}}-{\underline{i}}{\mid}{\geq}n}{\sum}cov(X_{\underline{i}},\;X_{\underline{j}}),\;{\mid}{\underline{x}}{\mid}=max({\mid}x_1{\mid},{\cdots},{\mid}x_d{\mid})\;for\;{\underline{x}}{\in}{\mathbb{R}}^d$. Our investigation implies and analogous result in the case associated random measure.