• Journal of the Korean Data and Information Science Society
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• 제16권3호
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• pp.705-712
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• 2005

Entropy is the basic concept of information theory. It is well defined for random varibles with known probability density function(pdf). For given data with unknown pdf, entropy should be estimated. Usually, estimation of entropy is based on the approximations. In this paper, we consider a kernel based approximation and compare it to the cumulant approximation method for several distributions. Monte carlo simulation for various sample size is conducted.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2009년도 학술발표회 초록집
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• pp.52-56
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• 2009

In this study a dynamic modeling scheme is presented to derive the probabilistic structure of soil water and plant water stress when subject to stochastic precipitation conditions. The newly developed model has the form of the Fokker-Planck equation, and its applicability as a model for the probabilistic evolution of the soil water and plant water stress is investigated under climate change scenarios. This model is based on the cumulant expansion theory, and has the advantage of providing the probabilistic solution in the form of probability distribution function (PDF), from which one can obtain the ensemble average behavior of the dynamics. The simulation result of soil water confirms that the proposed soil water model can properly reproduce the results obtained from observations, and it also proves that the soil water behaves with consistent cycle based on the precipitation pattern. The plant water stress simulation, also, shows two different PDF patterns according to the precipitation. Moreover, with all the simulation results with climate change scenarios, it can be concluded that the future soil water and plant water stress dynamics will differently behave with different climate change scenarios.

• 한국물환경학회지
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• 제25권1호
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• pp.112-119
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• 2009

Based on the study of soil water dynamics, this study is to suggest an advanced stochastic soil water model for future study for drought application. One distinguishable remark of this study is the derivation of soil water dynamic controling equation for 3-stage loss functions in order to understand the temporal behaviour of soil water with reaction to the precipitation. In terms of modeling, a model with rather simpler structure can be applied to regenerate the key characteristics of soil water behavior, and especially the probabilistic solution of the derived soil water dynamic equation can be helpful to provide better and clearer understanding of soil water behavior. Moreover, this study will be the future cornerstone of applying to more realistic phenomenon such as drought management.

• 한국경영과학회지
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• 제38권1호
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• pp.201-216
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• 2013

Diffusion is a basic mathematical tool for modern financial engineering. The theory of the estimation methods for diffusion models is an important topic of the financial engineering. Many researches have been tried to apply the likelihood estimation method for estimating diffusion models. However, the likelihood estimation method for diffusion is complicated and needs much amount of computing. In this paper we develop the estimation methods which are simple enough to be compared to the Euler approximation method, and efficient enough statistically to be compared to the likelihood estimation method. We devise pseudo-likelihood and propose the maximum pseudo-likelihood estimation methods. The pseudo-likelihoods are obtained by approximating the transition density with normal distributions. The means and the variances of the distributions are obtained from the delta expansion suggested by Lee, Song and Lee (2012). We compare the newly suggested estimators with other existing estimators by simulation study. From the simulation study we find the maximum pseudo-likelihood estimator has very similar properties with the maximum likelihood estimator. Also the maximum pseudo-likelihood estimator is easy to apply to general diffusion models, and can be obtained by simple numerical steps.

• 한국수자원학회논문집
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• 제42권6호
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• pp.433-443
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• 2009

토양수분에 관한 관심이 급증하면서 토양수분의 시공간적 특성을 이해하고자 하는 연구가 최근 꾸준히 일어나고 있다. 토양수분의 보다 나은 이해를 위해, 본 연구에서는 이에 대한 동역학을 추계학적 기법을 이용하여 기후변화에 따른 영향평가에 대한 적용을 염두에 둔 추계학적 토양수분모형을 제시하고자 하였다. 보다 현실적인 적용을 위하여 손실항을 세 가지로 구분하여 고려하였고 강우의 추계학적인 특성 역시 고려하였다. 모의 결과 본 연구에서 유도한 토양수분 모형으로 관측 자료를 적절하게 재현 할 수 있으며 토양수분이 계절별로 강수의 패턴에 따라 일정한 순환의 형태를 가짐을 재현하였다. 또한 CGCM3.1 자료를 이용한 미래 토양수분 상태 예측으로, 토양수분의 변동성이 현재보다 커질 것으로 예측되었다.