• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.337-342
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• 2005

The present paper establishes the improved version of central limit theorem for sums of level-continuous fuzzy set-valued random variables as a generalization of central limit theorem for sums of independent and identically distributed set-valued random variables.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.65-74
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• 2002

In this paper we investigate an origin and development of the classical theory of probability. And we also investigate the law of large numbers and central limit theorem which are very important in tile probability theory.

• Journal of Intelligence and Information Systems
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• v.28 no.2
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• pp.19-31
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• 2022

In Machine learning, we usually divide the entire data into training data and test data, train the model using training data, and use test data to determine the accuracy and generalization performance of the model. In the case of models with low generalization performance, the prediction accuracy of newly data is significantly reduced, and the model is said to be overfit. This study is about a method of generating training data based on central limit theorem and combining it with existed training data to increase normality and using this data to train models and increase generalization performance. To this, data were generated using sample mean and standard deviation for each feature of the data by utilizing the characteristic of central limit theorem, and new training data was constructed by combining them with existed training data. To determine the degree of increase in normality, the Kolmogorov-Smirnov normality test was conducted, and it was confirmed that the new training data showed increased normality compared to the existed data. Generalization performance was measured through differences in prediction accuracy for training data and test data. As a result of measuring the degree of increase in generalization performance by applying this to K-Nearest Neighbors (KNN), Logistic Regression, and Linear Discriminant Analysis (LDA), it was confirmed that generalization performance was improved for KNN, a non-parametric technique, and LDA, which assumes normality between model building.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.197-210
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• 2005

In Korea, mathematics education has been taken according to the 7th national mathematics curriculum renovated by the Ministry of Education and Human Resources Development announcement in 1997. The education of probability and Statistics has been carried out as a part of this curriculum. We analyze and compare mathematics 1 textbooks for 11-12 grade students. Descriptions of random variable, sample variance and sample standard deviation, distribution of sample mean, and etc. which are on some textbooks, are misleaded in school education. We suggest the unbiased estimator of sample variance in accordance with textbooks and central limit theorem of sample mean under normal population.

• The Korean Journal of Applied Statistics
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• v.12 no.2
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• pp.671-681
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• 1999

이항분포의 정규근사는 중심극한정리의 한 예로서 자주 언급되는데 정규근사를 하기 위한 시행회수 n과 성공률 p에 대한 판정기준들이 다수 제시되고 있는 데, 본 논문은 이러한 판정기준들에 대하여 제약조건의 강도와 평균오차한계를 비교, 검토하였다.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.779-786
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• 2009

Lotto is one of the most popular lottery games in the world. In korea the lotto considers numbers 1, 2,..., 45 from which 6 numbers are drawn randomly, without replacement. The profits from the lotto supports social welfare. However, there has been a suspicion that the choice of the winning numbers might not be random. In this study, we applied the randomness test developed by Coronel-Brizio et al. (2008) to the historical korean lotto data to see if the drawing process is random. The result of our study shows that the process was random during two periods under the management of different business companies and of price changes, respectively.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.371-382
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• 2002

경계를 통해서 유출되는 에너지 양을 측정하는 전체열용량 (total heat energy content)은 짧은 시간 극한에서 점근식 을 갖는데 그 계수 $\beta$$_{n}$은 기하학적 양에 의해서 국소적으로 계산 가능한 스펙트럼 불변량이다. 이 논문에서는 열용량 점근에 대하여 저자의 관심사 항을 중심으로 최근까지 연구되어진 바에 대하여 검토 및 정리해 보고자 한다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.385-388
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• 2004

The present paper establish the improved version of central limit theorem for sums of level-continuous fuzzy random variables as a generalization of central limit theorem for sums of independent and identically distributed random sets.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.13 no.4
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• pp.20-29
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• 2014

Density is applied both three major macroscopic traffic variables (traffic volume, speed, and density) and two measures of effectiveness (MOE) for level of service (LOS) on highway (density and V/C). Especially, it is known for the most accurate MOE on evaluating the LOS of highway. Despite such importance, there is a lack of study on density relatively than other variables for its difficulty of measurement. Existing density estimation methods have some limitations such as density values of same traffic flow vary with collecting time. In this study, we researched actual density measuring method with panoramic image, after each CCTV images in the Sapaesan Tunnel on Seoul Ring Expressway are matched into one panoramic image. Analysis through the Central Limit Theorem shows that density of 24 1 km-images, which means 24 second, applies traffic situation well. That is to say that reasonable density value regardless of collecting time, and practical density which represents actual traffic flow can be taken in case of measuring density by suggested collecting cycle.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2014.06a
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• pp.41-42
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• 2014

최근 우리나라에서는 새로운 항만설계 혹은 변경 등을 함에 있어 해상교통안전진단을 우선적으로 실시하여 해상교통의 안전을 도모하고 있다. 이 해상교통안전진단은 자연환경 및 해상교통조사, 선박조종시뮬레이션, 해상교통류 시뮬레이션, 계류안전성, 그리고 안전대책 등으로 구성되어 있다. 그 중 선박조종과 관련된 선박조종시뮬레이션이 아주 중요하다. 이것은 해당 항만에서 선박 조종을 담당하는 도선사 혹은 선장들에게 직접적인 관련이 있기 때문이다. 선박조종시뮬레이션에서 근접도 평가는 항로 혹은 접이안 조선의 안전도를 평가하는 중요한 요소이다. 그러나 근접도 평가는 시뮬레이션의 횟수를 얼마 이상으로 할 때 제대로 된 평가를 할 수 있는가 하는 점은 밝혀져 있지 않다. 중심극한정리에 따르면 30회 이상이면 표본 집단은 정규분포를