• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.643-660
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• 2004

In this paper, we give a new formula between the conditional Wiener integral E(F｜X), the conditional Wiener integral of F given X, and the integral with respect to a measure-valued measure, a kind of Bartle integral. Using this formula, we give some examples of evaluation of E(F｜X).

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.225-234
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• 2014

We propose a novel hierarchical clustering for distribution valued dissimilarities. Analysis of large and complex data has attracted significant interest. Symbolic Data Analysis (SDA) was proposed by Diday in 1980's, which provides a new framework for statistical analysis. In SDA, we analyze an object with internal variation, including an interval, a histogram and a distribution, called a symbolic object. In the study, we focus on a cluster analysis for distribution valued dissimilarities, one of the symbolic objects. A hierarchical clustering has two steps in general: find out step and update step. In the find out step, we find the nearest pair of clusters. We extend it for distribution valued dissimilarities, introducing a measure on their order relations. In the update step, dissimilarities between clusters are redefined by mixture of distributions with a mixing ratio. We show an actual example of the proposed method and a simulation study.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.259-268
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• 2013

In this paper, we define the Banach-valued strong $M_{\alpha}$-integral and study the primitive of the strong $M_{\alpha}$-integral in terms of the $M_{\alpha}$-variational measures. We also prove that every function of bounded variation is a multiplier for the strong $M_{\alpha}$-integral.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.27-37
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• 2000

In this paper, we will introduce the pan-dual generalized fuzzy integral of a commutative isotonic semigroup-valued functions, which is generalized of the (DG) fuzzy integral and investigate the fundamental properties of this kind of fuzzy integral.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.173-183
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• 1998

In this paper, we introduce the pan-generalized fuzzy integral of a commutative isotonic semigroup-valued function, which is generalization of the (G) fuzzy integral and investigate the fundamental properties of this kind of fuzzy integral.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.1-10
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• 2007

In this paper, we define and study the Banach-valued C-integral and strong C-integral, We prove that the C-integral and the strong C-integral are equivalent if and only if the Banach space is finite dimensional. We also study the primitive of the strong C-integral in terms of the C-variational measures.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.4
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• pp.323-326
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• 2002

In this paper, we consider Choquet integrals of interval number-valued functions(simply, interval number-valued Choquet integrals). Then, we prove convergence theorem for interval number-valued Choquet integrals with respect to an autocontinuous fuzzy measure.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.29-42
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• 2018

We combine the integer-valued GARCH(1, 1) model with a generalized regime-switching model to propose a dynamic count time series model. Our model adopts Markov-chains with time-varying dependent transition probabilities to model dynamic count time series called the generalized regime-switching integer-valued GARCH(1, 1) (GRS-INGARCH(1, 1)) models. We derive a recursive formula of the conditional probability of the regime in the Markov-chain given the past information, in terms of transition probabilities of the Markov-chain and the Poisson parameters of the INGARCH(1, 1) process. In addition, we also study the forecasting of the Poisson parameter as well as the cumulative impulse response function of the model, which is a measure for the persistence of volatility. A Monte-Carlo simulation is conducted to see the performances of volatility forecasting and behaviors of cumulative impulse response coefficients as well as conditional maximum likelihood estimation; consequently, a real data application is given.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.779-789
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• 2011

In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.59-67
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• 1994

Let (${\Omega},{\Sigma},{\mu}$) be a measure space. A function $f:{\Omega}{\rightarrow}X$ is said to be equioscillated if for each set $A{\in}{\Sigma}$ of positive measure and for each ${\epsilon}$ > 0, there is a measurable subset B of A of positive measure such that the inequality s$sup_{{\omega}{\in}B}x^*f({\omega})-inf_{{\omega}{\in}B}x^*f({\omega})$ < ${\epsilon}$ holds for every $x^*$ with $||x^*||{\leq}1$. Strong measurability of a vector valued function is characterized using equioscillation.