• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• Journal of the Korean Statistical Society
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• v.35 no.3
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• pp.239-250
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• 2006

A $2{\times}2$ crossover design including carryover effect is considered for assessment of population bioequivalence of two drug formulations in a Bayesian framework. In classical analysis, it is complex to deal with the carryover effect since the estimate of the drug effect is biased in the presence of a carryover effect. The proposed method in this article uses uninformative priors and vague proper priors for objectiveness of priors and the posterior probability distribution of the parameters of interest is derived with given priors. The posterior probabilities of the hypotheses for assessing population bioequivalence are evaluated based on a Markov chain Monte Carlo simulation method. An example with real data set is given for illustration.

• Toxicological Research
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• v.32 no.1
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• pp.5-8
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• 2016

Risk assessment is the process of quantifying the probability of a harmful effect to individuals or populations from human activities. Mechanistic approaches to risk assessment have been generally referred to as systems toxicology. Systems toxicology makes use of advanced analytical and computational tools to integrate classical toxicology and quantitative analysis of large networks of molecular and functional changes occurring across multiple levels of biological organization. Three presentations including two case studies involving both in vitro and in vivo approaches described the current state of systems toxicology and the potential for its future application in chemical risk assessment.

• The Mathematical Education
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• v.3 no.10
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• pp.7-20
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• 1965

One of the prerequisites for the improvement of the teaching of mathematics in our country is an improved curriculum-one which takes account of the increasing use of mathematics in science and technology and in other areas of knowledge and at the same time one which reflects recent advances in mathematics itself. In the new curriculum of mathematics, we have found the problems to teach the concept of sets at secondary level. The idea of a set is the most fundamental one in mathematics. So, this thesis contains the studies of the systematic analysis of sets in dealing with the traditional textbook. The scope of the work is limited to the fundamental ideas, and so it merely touches on the topics of the Concpets, Operations, Cardinal Numbers, Application of Logic, one-to-one Correspondence, Probability and so on. It provides only the essentials, definitions, proofs and some example which are already known and understood in their traditional context. It also presents at the appropriate stages the concepts required (illustrated by examples) in a much clearer fashion than classical teaching does. To compete a study of the sets covered in the textbook of each year, greater detail is needed at the appropriate level.

• Proceedings of the Korea Society for Simulation Conference
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• 1999.04a
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• pp.70-79
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• 1999

Importance Sampling (IS) has been applied to accelerate the occurrence of rare events. However, it has a drawback of effective biasing scheme to make the estimator from IS unbiased. Adaptive Importance Sampling (AIS) employs an estimated sampling distribution of IS to the systems of interest during the course of simulation. We propose Nonparametric Adaptive Importance Sampling (NAIS) technique which is nonparametrically modified version of AIS and test it to estimate a probability of rare event in M/M/1 queueing model. Comparing with classical Monte Carlo simulation, the computational efficiency and variance reductions gained via NAIS are substantial. A possible extension of NAIS regarding with random number generation is also discussed.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.11a
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• pp.877-880
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• 2006

The stochastic nature of the tensile strength of concrete is investigated theoretically and experimentally. The tensile strength of concrete was modeled by a theory based on the failure probability of a crack arbitrarily oriented within a concrete body. According to this model, the stochastic nature of the tensile strength depend on the current stress state. This aspect was checked experimentally using a classical three point bend specimen and a rectangular plate specimen loaded at the center. It has been known that the biaxial strength is no different from the uniaxial strength. However, if the region where the tensile strength is constant gets small, the biaxial tensile strength increases and its stochastical variation decreases.

• Journal of Information Processing Systems
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• v.16 no.1
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• pp.145-154
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• 2020

Maximum likelihood (ML) is the best estimator asymptotically as the number of training samples approaches infinity. This paper deduces an adaptive algorithm for blind signal processing problem based on gradient optimization criterion. A parametric density model is introduced through a parameterized generalized distribution family in ML framework. After specifying a limited number of parameters, the density of specific original signal can be approximated automatically by the constructed density function. Consequently, signal separation can be conducted without any prior information about the probability density of the desired original signal. Simulations on classical biomedical signals confirm the performance of the deduced technique.

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.4
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• pp.384-391
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• 2000

Most of the previous works on classical location models are based on the assumption that the value(or utilities) of inventory remains constants over time. In this study a special case of location problem is studied for both ameliorating and deteriorating items in two-echelon supply-chain management such as agricultural and fishery products. The objective of this study is to determine the minimum number of storage facilities among a discrete set of location sites so that the probability for each customer to be covered is not less than a critical value. We have formulated this problem using stochastic set-covering problem which can be solved by 0-1 programming method. Also we developed a computer program and applied to a set of problems for fish culture storage and distribution centers and the sample results well show the impact of ameliorating and deteriorating rate on the location problem. For the further study, a graphical user-interface with visualization for input and output is needed to be developed.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.305-312
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• 2005

In the cluster analysis, Hotelling's $T^2$ can be used to estimate the unknown number of clusters based on the idea of multiple comparison procedure. Especially, its threshold is obtained according to the probability of committing the type one error. Examples are used to compare Hotelling's $T^2$ with other classical location test statistics such as Sum-of-Squared Error and Wilks' $\Lambda$ The hierarchical clustering is used to reveal the underlying structure of the data. Also related criteria are reviewed in view of both the between variance and the within variance.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.473-495
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• 2019

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.