• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.407-416
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• 1997

Suppose that { $X_{i}$ } is a stationary AR(1) process and { $Y_{j}$ } is an ARX process with { $X_{i}$ } as exogeneous variables. Let $Y_{j}$ $^{*}$ be the stochastic process which is the sum of $Y_{j}$ and a nonstochastic trend. In this paper we consider the problem of estimating the conditional probability that $Y_{{n+1}}$$^{*}$ is bigger than $X_{{n+1}}$, given $X_{1}$, $Y_{1}$$^{*}$,..., $X_{n}$ , $Y_{n}$ $^{*}$. As an estimator for the tolerance probability, an Mann-Whitney statistic based on least squares residuars is suggested. It is shown that the deviations between the estimator and true probability are stochatically bounded with $n^{{-1}$2}/ order. The result may be applied to the stress-strength reliability theory when the stress and strength variables violate the classical iid assumption.umption.n.

• International Journal of Reliability and Applications
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• 제3권1호
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• pp.37-50
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• 2002

Simultaneous estimation of accuracy and probability corresponding to a prediction interval is considered in this study. Traditional application of confidence interval forecasting consists in evaluation of interval limits for a given significance level. The wider is this interval, the higher is probability and the lower is the forecast precision. In this paper a measure of stochastic forecast accuracy is introduced, and a procedure for balanced estimation of both the predicting accuracy and confidence probability is elaborated. Solution can be obtained in an optimizing approach. Suggested method is applied to constructing confidence intervals for parameters estimated by normal and t distributions

• 대한수학회보
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• 제47권1호
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• pp.39-51
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• 2010

In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler [19] and other results of independent problems. The results also generalizes those of Bae and Choi [3] to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.623-633
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• 2012

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n|n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_n|n{\geq}1$} is said to be conditionally negatively associated given $\mathcal{F}$ if for every pair of disjoint subsets A and B of {1, 2, ${\cdots}$, n}, $Cov^{\mathcal{F}}(f_1(X_i,i{\in}A),\;f_2(X_j,j{\in}B)){\leq}0$ a.s. whenever $f_1$ and $f_2$ are coordinatewise nondecreasing functions. We extend the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality from negative association to conditional negative association of random variables. In addition, some corollaries are given.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1033-1047
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• 2009

In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.

• 대한수학회지
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• 제33권4호
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• pp.793-799
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• 1996

Let $A_1, A_2, \cdots, A_m$ be a sequence of events on a given probability space and let $X_m(A)$ be the number of those A's which occur.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.677-686
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• 1999

In this paper we introduce a class of moving-average(MA) sequences of multivariate random vectors with geometric marginals. The theory of positive dependence is used to show that in various cases the class of MA sequences consists of associated random variables. We utilize positive dependence properties to obtain weakly probability inequality of the multivariate processes.

• 대한전자공학회논문지SP
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• 제45권6호
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• pp.57-63
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• 2008

본 논문에서는 웨이블릿 영역에서 이변수 가우스 확률밀도함수를 이용하여 잡음을 효과적으로 제거하는 방법을 제안한다. 본 논문의 방법은 웨이블릿 영역의 스케일간의 관계에 대한 통계적 모델을 이변수 가우스 확률분포로 설정하고, 이에 대한 베이즈 추정법을 통하여 잡음 제거를 수행한다. 베이즈 추정법을 위한 통계 파라메터는 $H{\ddot{o}}lder$ 부등식을 이용하여 근사적으로 추정한다. 실험 결과를 통하여 본 논문의 방법이 기존의 이변수 사전 확률모델을 이용한 잡음 제거 방법에 비하여 우수한 결과를 보여 준다는 것을 알 수 있다.

• 한국항공우주학회지
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• 제33권2호
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• pp.32-38
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• 2005

본 연구에서는 근사모델을 이용하여 설계공간의 타당성을 높일 수 있는 방법을 제시하였다. 이때 설계공간을 이동시키기 위한 기준으로 Chebyshev Inequality를 사용하였다. 이를 공탄성을 고려한 항공기 익형 설계문제에 적용함으로써 타당성이 크게 향상됨을 확인하였으며 이렇게 구한 설계공간 내에서 최적화를 수행함으로써 보다 우수한 최적값도 얻을 수 있었다. 즉 설계공간 내에서 주어진 제약조건을 만족할 확률이 증가하였으며, 설계공간을 이동시킴으로써 보다 우수한 최적점이 설계공간 내에 포함되었다고 할 수 있다. 또한 이 과정에서 반응면 모델과 크리깅 모델, 두 가지 근사모델을 사용하여 정확성과 효율성, 실험점에 대한 강건성 등을 비교하였으며, 본 연구에서 설계한 문제의 경우 비교적 선형적인 특징으로 인해 반응면이 보다 우수한 결과를 보여줌을 확인하였다.

• 보건행정학회지
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• 제28권4호
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• pp.339-351
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• 2018

Background: The purpose of this study is to estimate empirically whether there is a difference in medical use among income groups, and if so, how much. This study applies econometric model to the most recent year of Korean Medical Panel, 2015. The model consists of outpatient service and inpatient service models. Methods: The probit model is applied to the model which indicate whether or not the medical care has been used. Two step estimation method using maximum likelihood estimation is applied to the models of outpatient visits, hospital days, and outpatient and inpatient out-of-pocket cost models, with disconnected selection problems. Results: The results show that there was the inequality favorable to the low income group in medical care use. However, after controlling basic medical needs, there were no inequities among income groups in the outpatient visit model and the model of probability of inpatient service use. However, there were inequities favorable to the upper income groups in the models of probability of outpatient service use and outpatient out-of-pocket cost and the models of the number of length of stay and inpatient out-of-pocket cost. In particular, it shows clearly how the difference in outpatient service and inpatient service utilizations by income groups when basic medical needs are controlled. Conclusion: This means that the income contributes significantly to the degree of inequality in outpatient and inpatient care services. Therefore, the existence of medical care use difference under the same medical needs among income groups is a problem in terms of equity of medical care use, so great efforts should be made to establish policies to improve equity among income groups.