• Journal of the Korean Data and Information Science Society
• /
• v.16 no.3
• /
• pp.705-712
• /
• 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.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2009.05a
• /
• pp.52-56
• /
• 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.

• Journal of Korean Society on Water Environment
• /
• v.25 no.1
• /
• pp.112-119
• /
• 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.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.38 no.1
• /
• pp.201-216
• /
• 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.

• Journal of Korea Water Resources Association
• /
• v.42 no.6
• /
• pp.433-443
• /
• 2009

For the better understanding of the temporal characteristics of soil water, this study is to suggest a stochastic soil water model and to apply it for impact assessment of climate change. The loss function is divided into 3 stages for more specified comprehension of the probabilistic behavior of soil water, and especially, the soil water model considering the stochastic characteristics of precipitation is developed in order to consider the variation of climatic factors. The simulation result of soil water model confirms that the proposed soil water model can re-generate the observation properly, and it also proves that the soil water behaves with consistent cycle based on the precipitation pattern. Moreover, with the simulation results with a climate change scenario, it can be predicted that the future soil water will have higher variations than present soil water.