• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.419-427
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• 2004

In this paper we establish the Hajeck-Renyi type inequality and derive the strong law of large numbers for asymptotically quadrant sub-independent random variables.

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• 제3권2호
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• pp.84-96
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• 2022

Most of the islands of Korea are distributed in the South and West Sea, and it consists of independent small stream. As a result, the fish community that inhabits the island's stream is isolated from the mainland and other island. This study utilized a Self-Organizing Map (SOM) and a random forest model to analyze the relationship between environmental variables and fish communities inhabiting islands in South Korea. Through the SOM analysis, the fish communities were divided into three clusters, and there were differences in biotic and abiotic factors between these groups. Cluster I consisted of sites with relatively larger island areas and a higher number of species and population. It was found that 15 out of 16 indicator species were included. Meanwhile, the remaining clusters had fewer species and populations. Cluster II, especially, showed the lowest impact from physical variables such as water width and depth. As a result of predicting the species richness using the random forest model, physical variables in habitats, such as stream width and water depth, had a relatively higher importance on species richness. On the other hand, forest area was the most important variables for predicting Shannon diversity, followed by maximum water depth, and gravel. The results suggest that this study can be used as basic data for establishing a stream ecosystem management strategy in terms of conservation and protection of biological resources in streams of islands.

• 한국콘텐츠학회논문지
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• 제6권5호
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• pp.29-34
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• 2006

본 연구에서는, Banach 공간의 값을 갖는 확률요소들의 합 $S_n=\sum_{i=1}^nV-i$ 수렴하는 경우에, Tail 합 $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$에 대한 대수의 법칙을 고찰하여 $S_n$이 하나의 확률변수 S로 수렴하는 속도를 연구한다. 좀 더 구체적으로 말하자면, 확률변수들의 Tail 합과 확률요소들의 Tail 합에 대한 극한 성질의 유사성을 연구하여, Banach 공간에서 독립인 확률요소들의 Tail 합에 대한 약 대수의 법칙과 하나의 수렴법칙이 동등함을 기술하는 기존의 정리를 다른 대체적인 방법으로 증명한다.

• Structural Engineering and Mechanics
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• 제38권2호
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• pp.171-193
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• 2011

One of the possible alternatives of simulation-based time-dependent reliability assessment of pre-stressed biconcave and biconvex cable trusses, the Monte Carlo method, is applied in this paper. The influence of an excessive deflection of cable truss (caused by creep of cables and rheologic changes) on its time-dependent serviceability is investigated. Attention is given to the definition of the basic random variables and their statistical functions (basic, mutually dependent random variables such as the pre-stressing forces of the bottom and top cable, structural geometry, the Young's modulus of elasticity of the cables, and the independent variables, such as permanent load, wind, snow and thermal actions). Then, the determination of the response of the cable truss to the loading effects, and the definition of the limiting values considering serviceability of the structure are performed. The potential of the method, using direct Monte Carlo technique for simulation-based time-dependent reliability assessment as a powerful tool, is emphasized. Results obtained by the First order reliability method (FORM) are compared with those obtained by the Monte Carlo simulation technique.

• 한국항공우주학회지
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• 제36권12호
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• pp.1186-1192
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• 2008

가스터빈 엔진 블레이드의 신뢰성을 해석하였다. 항복강도, 탄성계수, 엔진속도 및 기체온도를 서로 독립적인 확률변수로 가정하였다. 파손확률을 구하기 위하여 사용한 방법들 중에서 Advanced Mean Value Method가 가장 효율적임을 알 수 있었다. 동일한 평균과 표준편차를 갖는 정규, 대수정규 및 Weibull 분포로 확률변수 형상을 가정하였을 경우, 극한상태방정식의 누적분포함수는 확률변수 분포형상에 의하여 큰 영향을 받지 않음을 알 수 있었다. 확률변수의 표준편차에 대한 파손확률의 민감도는 기체온도의 경우에 가장 크다는 것을 알 수 있었다. 확률변수의 평균과 표준편차의 효과를 검토하였다. 기체온도의 평균과 엔진속도의 표준편차의 증가가 파손확률을 가장 크게 증가시킴을 알 수 있었다.

• 산업진흥연구
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• 제7권1호
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• pp.1-8
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• 2022

본 논문은 중도중단 데이터가 포함된 생존데이터의 경우 적용할 수 있는 기계학습 방법에 대해 살펴보았다. 우선 탐색적인 자료분석으로 각 특성에 대한 분포, 여러 특성들 간의 관계 및 중요도 순위를 파악할 수 있었다. 다음으로 독립변수에 해당하는 여러 특성들과 종속변수에 해당하는 특성(사망여부) 간의 관계를 분류문제로 보고 logistic regression, K nearest neighbor 등의 기계학습 방법들을 적용해본 결과 적은 수의 데이터이지만 통상적인 기계학습 결과에서와 같이 logistic regression보다는 random forest가 성능이 더 좋게 나왔다. 하지만 근래에 성능이 좋다고 하는 artificial neural network나 gradient boost와 같은 기계학습 방법은 성능이 월등히 좋게 나오지 않았는데, 그 이유는 주어진 데이터가 빅데이터가 아니기 때문인 것으로 판명된다. 마지막으로 Kaplan-Meier나 Cox의 비례위험모델과 같은 통상적인 생존분석 방법을 적용하여 어떤 독립변수가 종속변수 (t_i, δ_i)에 결정적인 영향을 미치는지 살펴볼 수 있었으며, 기계학습 방법에 속하는 random forest를 중도중단 데이터가 포함된 생존데이터에도 적용하여 성능을 평가할 수 있었다.

• 대한방사선기술학회지:방사선기술과학
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• 제43권6호
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• pp.495-502
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• 2020

In this study, the prevalence of osteoporosis was predicted based on 10 independent variables such as age, weight, and alcohol consumption and 4 tree-based machine-learning models, and the performance of each model was compared. Also the model with the highest performance was used to check the performance by clearing the independent variable, and Area Under Curve(ACU) was utilized to evaluate the performance of the model. The ACU for each model was Decision tree 0.663, Random forest 0.704, GBM 0.702, and XGBoost 0.710 and the importance of the variable was shown in the order of age, weight, and family history. As a result of using XGBoost, the highest performance model and clearing independent variables, the ACU shows the best performance of 0.750 with 7 independent variables. This data suggests that this method be applied to predict osteoporosis, but also other various diseases. In addition, it is expected to be used as basic data for big data research in the health care field.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.96.2-96
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• 2002

In this paper, a new method for the mixed image separation is presented using the independent component analysis, the innovation process, and the expectation-maximization. In general, the independent component analysis (ICA) is one of the widely used statistical signal processing scheme that represents the information from observations as a set of random variables in the form of linear combinations of another statistically independent component variables. In various useful applications, ICA provides a more meaningful representation of the data than the principal component analysis through the transformation of the data to be quasi-orthogonal to each other, which can be utilized in linear p...

• 충청수학회지
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• 제8권1호
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• pp.11-17
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• 1995

Let ${\tau}_a$ be the first time that a perturbed random walk with extended real-valued independent and identically distributed (i.i.d.) random variables crosses a constant boundary $a{\geq}0$. For the stopping times ${\tau}_a$ we investigate some basic properties and obtain its limiting distribution as $a{\rightarrow}{\infty}$ and an upper bound of the expected stopping times E(${\tau}_a$).