• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.89-102
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• 1994

A new method for approximating the average run length (ARL) of cumulative sum (CUSUM) chart is proposed. This method uses the conditional expectation for the test statistic before the stopping time and its asymptotic conditional density function. The values obtained by this method are compared with some other methods in normal and exponential case.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.21-34
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• 1999

In this paper, conditional expectation of a fuzzy random variable is introduced and its properties are investigated. Using this, we introduce the concept of fuzzy martingales and prove some convergence theorems which generalize te corresponding results for the classical martingales.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.52-56
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• 1994

When we have an i.i.d. sample of size n from a continuous distribution, the distribution truncated on the left at the rth order statistic plays an important role in the theoretical analysis of the Type 2 censored data. The charaterization of distributions by the average of the conditional expectation and the average of the conditional information concerning the truncated distribution is studied here.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.339-345
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• 2016

The set of priors in the representation of Choquet expectation is expressed as the one of equivalent martingale measures under some conditions. We show that the set of priors, $\mathcal{Q}_c$ in (1.1) is the same set of $\mathcal{Q}^{\theta}$ in (1.3).

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.119-126
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• 2010

In this paper, we find the formula for the analogue of Wiener measure over the subset of C[0, T] bounded by the sectionally differentiable functions, which is a generalization of Park and Skoug's results in [2].

• Proceedings of the Korean Nuclear Society Conference
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• 1998.10a
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• pp.53-53
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• 1998

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.33-40
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• 1994

The conditional expectation of a random variable in a multivariate normal random vector is a multiple linear regression on its predecessors. Using this fact, the least median of squares estimation method developed in a multiple linear regression is adapted to a multivariate data to identify influential observations. The resulting method clearly detect outliers and it avoids the masking effect.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1201-1212
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• 2016

Value at Risk (VaR) for market risk management is a favorite method used by financial companies; however, there are some problems that cannot be explained for the amount of loss when a specific investment fails. Conditional Tail Expectation (CTE) is an alternative risk measure defined as the conditional expectation exceeded VaR. Multivariate loss rates are transformed into a univariate distribution in real financial markets in order to obtain CTE for some portfolio as well as to estimate CTE. We propose multivariate CTEs using multivariate quantile vectors. A relationship among multivariate CTEs is also derived by extending univariate CTEs. Multivariate CTEs are obtained from bivariate and trivariate normal distributions; in addition, relationships among multivariate CTEs are also explored. We then discuss the extensibility to high dimension as well as illustrate some examples. Multivariate CTEs (using variance-covariance matrix and multivariate quantile vector) are found to have smaller values than CTEs transformed to univariate. Therefore, it can be concluded that the proposed multivariate CTEs provides smaller estimates that represent less risk than others and that a drastic investment using this CTE is also possible when a diversified investment strategy includes many companies in a portfolio.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.239-260
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• 2014

Non-stationary random vibration of linear structures with uncertain parameters is investigated in this paper. A time-domain explicit formulation method is first presented for dynamic response analysis of deterministic structures subjected to non-stationary random excitations. The method is then employed to predict the random responses of a structure with given values of structural parameters, which are used to fit the conditional expectations of responses with relation to the structural random parameters by the response surface technique. Based on the total expectation theorem, the known conditional expectations are averaged to yield the random responses of stochastic structures as the total expectations. A numerical example involving a frame structure is investigated to illustrate the effectiveness of the present approach by comparison with the power spectrum method and the Monte Carlo simulation method. The proposed method is also applied to non-stationary random seismic analysis of a practical arch bridge with structural uncertainties, indicating the feasibility of the present approach for analysis of complex structures.