• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.127-130
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• 2003

주변분포가 Laplace 분포인 세 가지 형태의 이변량 Laplace 분포를 연구한다. 각각의 이변량 Laplace 분포의 확률밀도함수와 누적분포함수를 유도하고, 분포의 그래프를 그려봄으로써 분포의 형태를 알아본다. 조건부 적률을 정리하여 조건부 첨도와 조건부 왜도를 구하고 분포의 성질을 파악한다. 상관계수를 구하여 다른 이변량 분포의 상관계수와 비교해 보았다. 그리고 정의된 분포함수를 응용하여 이변량 Laplace 분포를 따르는 난수벡터를 발생하는 알고리즘을 제안하였으며, 생성된 난수벡터의 표본으로부터 구한 표본평균과 중앙값의 분산-공분산 행렬식을 구하고 이변량 정규분포에 대응하는 행렬식과 비교 토론하였다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.5A
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• pp.855-862
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• 2001

본 논문에서는 백색잡음과 페이딩 환경하의 통신시스템의 성능평가시 백색잡음에 대해서만 모멘트 기법을 이용조건부 오류확률을 구하고 페이딩에 대해서는 해석적 접근방식을 취함으로써 전체적인 컴퓨터 수행시간을 획기적으로 개선시킬 수 있는 기법을 제안하고, 제안된 기법의 효율성을 컴퓨터 시뮬레이션 수행시간 비교를 통해 입증하였다. 현재 널리 사용되는 Monte Carlo 시뮬레이션 기법은 IS-95 순방향 채널과 같이 많은 샘플수를 필요로 하는 시스템에서 상당한 시뮬레이션 수행시간을 요구하게 된다. 이러한 문제점을 해결하기 위하여, 제안된 방식에서는 백색잡음하의 수신신호의 N차 모멘트를 측정하여 이산확률밀도함수를 구함으로써 수신신호의 확률적 특성을 모사하고, 이로부터 내삽법과 외삽법을 적용하여 조건부 누적확률분포함수를 산출함으로써 채널오류율을 구하게 된다. 그리고 페이딩 성능평가시 조건부 채널오류율을 이용하여 산출된 조건부 누적확률분포함수를 환경조건에 맞춘 후에 페이딩의 확률밀도함수와 수치 해석적으로 간단히 적분하여 성능평가를 함으로써 수행시간의 줄임과 동시에 정확한 채널오류율을 구하게 된다.

• Journal of the Korean Geotechnical Society
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• v.28 no.11
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• pp.5-16
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• 2012

Since geologic data are often sampled at sparse locations, it is important not only to predict attribute values at unsampled locations, but also to assess the uncertainty attached to the prediction. In this paper, the assessment of the local uncertainty of prediction for the depth to weathered soil was performed by using the indicator kriging. A conditional cumulative distribution function (ccdf) was first modeled, and then E-type estimate was computed for the spatial distribution of the depth to the weathered soil. Also, optimal estimate of spatial distribution for the depth to weathered soil was determined by using ccdf and loss function. The design procedure and method considering the minimum expected loss presented in this paper can be used in the decision-making process for geotechnical engineering design.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.987-994
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• 2011

From the point view of credit evaluation whose population is divided into the default and non-default state, two methods are considered to estimate conditional distribution functions: one is to estimate under the assumption that the data is followed the mixture normal distribution and the other is to use the kernel density estimation. The parameters of normal mixture are estimated using the EM algorithm. For the kernel density estimation, five kinds of well known kernel functions and four kinds of the bandwidths are explored. In addition, the corresponding ROC functions are obtained based on the estimated distribution functions. The goodness-of-fit of the estimated distribution functions are discussed and the performance of the ROC functions are compared. In this work, it is found that the kernel distribution functions shows better fit, and the ROC function obtained under the assumption of normal mixture shows better performance.

• Journal of the Korean Geographical Society
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• v.44 no.3
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• pp.395-409
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• 2009

The objective of this paper is to illustrate that kriging can provide an effective framework both for integrating remote sensing data and for uncertainty modeling through a case study of sediment grain size mapping with remote sensing data. Landsat TM data which show reasonable relationships with grain size values are used as secondary information for sediment grain size mapping near the eastern part of Anmyeondo and Cheonsuman bay. The case study results showed that uncertainty attached to prediction at unsampled locations was significantly reduced by integrating remote sensing data through the analysis of conditional variance from conditional cumulative distribution functions. It is expected that the kriging-based approach presented in this paper would be efficient integration and analysis methodologies for any environmental thematic mapping using secondary information as well as sediment grain size mapping.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.98-98
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• 2016

본 연구에서는 유입량의 불확실성을 고려하여 미래 저수량을 확률론적으로 예측하였다. 월별 유입량을 표본으로 한 확률밀도함수를 핵밀도함수(kernel function)를 이용하여 추정하고, 추정된 확률분포로 월별 유입량을 모의 발생하였다. 모의 발생된 유입량을 통해 연속적인 조건부 확률을 산정하였고, 이의 누적확률분포(F(x))는 해당 저수량에 도달하지 못할 확률, 즉 실패확률을 의미하므로 1-F(x)로 해당 저수량 이상을 확보할 수 있는 확률을 산정하였다. 보령댐을 대상으로 분석한 결과 2016년 2월 말 저수량 27.8 백만$m^3$ 기준으로 3월부터 6월까지 정상용수공급환원 기준 저수량을 만족할 확률이 각각 2.3%, 12.5%, 24.2%, 33.5%로 나타났다. 지역적 가뭄에 대응하기 위해 하천유지용수 감량, 용수 대체공급, 자율 급수조정 및 금강-보령댐 도수로를 이용한 용수공급으로 20.6만$m^3/day$의 용수가 비축될 경우, 정상용수공급환원 기준 저수량을 만족할 확률이 10.2%, 40.3%, 73.8%, 78.7%로 용수비축의 효과가 크게 나타나는 것을 확인하였다. 저수량의 확률론적 예측을 통해 미래 저수량의 확률적 발생가능성을 추정할 수 있으며, 가뭄이 발생할 경우, 가뭄 대응효과를 정량적으로 나타낼 수 있어 가뭄 위험 상황 전달 및 용수공급조정 의사결정 시 활용할 수 있을 것으로 판단된다.

• Journal of the Korean earth science society
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• v.32 no.3
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• pp.249-264
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• 2011

A multi-Gaussian kriging approach extended to space-time domain is presented for uncertainty modeling as well as time-series mapping of environmental variables. Within a multi-Gaussian framework, normal score transformed environmental variables are first decomposed into deterministic trend and stochastic residual components. After local temporal trend models are constructed, the parameters of the models are estimated and interpolated in space. Space-time correlation structures of stationary residual components are quantified using a product-sum space-time variogram model. The ccdf is modeled at all grid locations using this space-time variogram model and space-time kriging. Finally, e-type estimates and conditional variances are computed from the ccdf models for spatial mapping and uncertainty analysis, respectively. The proposed approach is illustrated through a case of time-series Particulate Matter 10 ($PM_{10}$) concentration mapping in Incheon Metropolitan city using monthly $PM_{10}$ concentrations at 13 stations for 3 years. It is shown that the proposed approach would generate reliable time-series $PM_{10}$ concentration maps with less mean bias and better prediction capability, compared to conventional spatial-only ordinary kriging. It is also demonstrated that the conditional variances and the probability exceeding a certain thresholding value would be useful information sources for interpretation.

• Journal of the Korean Geotechnical Society
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• v.28 no.1
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• pp.17-27
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• 2012

Since geologic data are often sampled at sparse locations, it is important not only to predict attribute values at unsampled locations but also to assess the uncertainty attached to the prediction. In this study the assessment of the local uncertainty of prediction for the thickness of the consolidation layer was performed by using the indicator approach. A conditional cumulative distribution function (ccdf) was first modeled, and then E-type estimates and the conditional variance were computed for the spatial distribution of the thickness of the consolidation layer. These results could be used to estimate the spatial distribution of secondary compression and to assess the local uncertainty of secondary compression for Songdo New City.

• Journal of Korea Water Resources Association
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• v.49 no.4
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• pp.275-282
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• 2016

The objective of this study is to propose a new method to determine the drought event and the design drought severity. In order to define a drought event from precipitation data, theory of run was applied with the cumulative rainfall deficit. When we have a large amount of rainfall over the threshold level, in this study, we compare with the previous cumulative rainfall deficit to determine whether the drought is relieved or not. The recurrence characteristics of the drought severity on the specific duration was analyzed by the conditional bivariate copula function and confidence intervals were estimated to quantify uncertainties. The methodology was applied to Seoul station with the historical dataset (1909~2015). It was observed that the past droughts considered as extreme hydrological events had from 10 to 50 years of return period. On the other hand, the current on-going drought event started from 2013 showed the significantly higher return period. It is expected that the result of this study may be utilized as the reliable criteria based on the concept of return period for the drought contingency plan.

• Journal of the Korean earth science society
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• v.31 no.4
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• pp.301-312
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• 2010

Geochemical data have been regarded as one of the important environmental variables in the environmental management. Since they are often sampled at sparse locations, it is important not only to predict attribute values at unsampled locations, but also to assess the uncertainty attached to the prediction for further analysis. The main objective of this paper is to exemplify how indicator geostatistics can be effectively applied to geochemical data processing for providing decision-supporting information as well as spatial distribution of the geochemical data. A whole geostatistical analysis framework, which includes probabilistic uncertainty modeling, classification and risk analysis, was illustrated through a case study of cadmium mapping. A conditional cumulative distribution function (ccdf) was first modeled by indicator kriging, and then e-type estimates and conditional variance were computed for spatial distribution of cadmium and quantitative uncertainty measures, respectively. Two different classification criteria such as a probability thresholding and an attribute thresholding were applied to delineate contaminated and safe areas. Finally, additional sampling locations were extracted from the coefficient of variation that accounts for both the conditional variance and the difference between attribute values and thresholding values. It is suggested that the indicator geostatistical framework illustrated in this study be a useful tool for analyzing any environmental variables including geochemical data for decision-making in the presence of uncertainty.