• 통합자연과학논문집
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• 제15권1호
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• pp.9-18
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• 2022

This research examines the power of bootstrap two-sample test, and compares it with the powers of two-sample t-test and Wilcoxon rank sum test, through simulation. For simulation work, a positively skewed and heavy tailed distribution was selected as a population distribution, the chi-square distributions with three degrees of freedom, χ²₃. For two independent samples, the fist sample was selected from χ²₃. The second sample was selected independently from the same χ²₃ as the first sample, and calculated d+ax for each sampled value x, a randomly selected value from χ²₃. The d in d+ax has from 0 to 5 by 0.5 interval, and the a has from 1.0 to 1.5 by 0.1 interval. The powers of three methods were evaluated for the sample sizes 10,20,30,40,50. The null hypothesis was the two population medians being equal for Bootstrap two-sample test and Wilcoxon rank sum test, and the two population means being equal for the two-sample t-test. The powers were obtained using r program language; wilcox.test() in r base package for Wilcoxon rank sum test, t.test() in r base package for the two-sample t-test, boot.two.bca() in r wBoot pacakge for the bootstrap two-sample test. Simulation results show that the power of Wilcoxon rank sum test is the best for all 330 (n,a,d) combinations and the power of two-sample t-test comes next, and the power of bootstrap two-sample comes last. As the results, it can be recommended to use the classic inference methods if there are widely accepted and used methods, in terms of time, costs, sometimes power.

• International Journal of Contents
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• 제3권1호
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• pp.1-8
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• 2007

The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. Although, multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of the distributions. The computation methods we adopted are exact and no interpolations are involved.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권6호
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• pp.2302-2316
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• 2015

We propose an efficient method of extracting targets within a region of interest in non-homogeneous infrared images by using a principal component analysis (PCA) plane and adaptive Gaussian kernel. Existing approaches for extracting targets have been limited to using only the intensity values of the pixels in a target region. However, it is difficult to extract the target regions effectively because the intensity values of the target region are mixed with the background intensity values. To overcome this problem, we propose a novel PCA based approach consisting of three steps. In the first step, we apply a PCA technique minimizing the total least-square errors of an IR image. In the second step, we generate a binary image that consists of pixels with higher values than the plane, and then calculate the second derivative of the sum of the square errors (SDSSE). In the final step, an iteration is performed until the convergence criteria is met, including the SDSSE, angle and labeling value. Therefore, a Gaussian kernel is weighted in addition to the PCA plane with the non-removed data from the previous step. Experimental results show that the proposed method achieves better segmentation performance than the existing method.

• 한국정보통신학회논문지
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• 제19권2호
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• pp.450-454
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• 2015

본 논문에서는 평면상에 가중치를 가진 점들이 주어질 때, 임의의 상수 r에 대해서 변의 길이 r인 정사각형 영역을 고려해서 이 안에 속하는 점들의 가중치 합이 최대가 되는 영역을 찾고자 한다. 변의 길이가 정해져 있지 않은 경우에 임의의 사각형 영역을 찾는 문제에 대한 연구가 있었다. 본 논문에서는 상수 r이 주어질 때, 변의 길이 r인 정사각형 영역을 찾는 문제를 다룬다. 우리는 동적 환경 하에서의 일차원 문제를 풀고, 이를 이용해서 O(nlogn+rn) 시간 복잡도를 갖는 알고리즘을 제안한다.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제21권1호
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• pp.51-64
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• 2007

본 연구에서는 유추를 바탕으로 삼각형의 코사인정리를 n각형으로 일반화시키고, 이를 벡터를 이용하여 증명할 것이다. 이를 통해, 수학교과의 내용을 유추를 통해 확장하는 한 예를 제시할 것이며, 수학 영재 교육에서 수학적 사고(특히 일반화, 유추)를 계발 육성하기 위한 교수-학습 자료로 활용할 수 있을 것으로 기대된다.

• Journal of the Korean Data and Information Science Society
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• 제17권2호
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• pp.661-668
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• 2006

There have been some controversies on the use of the coefficient of determination for linear no-intercept model. One definition of the coefficient of determination, $R^2={\sum}\;{\widehat{y^2}}\;/\;{\sum}\;y^2$, is being widely accepted only for linear no-intercept models though Kvalseth (1985) demonstrated some possible pitfalls in using such $R^2$. Main objective of this note is to report that $R^2$ is not a desirable measure of fit for the no-intercept linear model. In fact it is found that mean square error(MSE) could replace $R^2$ efficiently in most cases where selection of no-intercept model is at issue.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2006년도 춘계공동학술대회 논문집
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• pp.1677-1683
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• 2006

Color image segmentation is useful for fast retrieval in large image database. For that purpose, new image segmentation technique based on the probability of pixel distribution in the image is proposed. Color image is first divided into R, G, and B channel images. Then, pixel distribution from each of channel image is extracted to select to which it is similar among the well known probabilistic distribution function-Weibull, Exponential, Beta, Gamma, Normal, and Uniform. We use sum of least square error to measure of the quality how well an image is fitted to distribution. That P.d.f has minimum score in relation to sum of square error is chosen. Next, each image is quantized into 4 gray levels by applying thresholds to the c.d.f of the selected distribution of each channel. Finally, three quantized images are combined into one color image to obtain final segmentation result. To show the validity of the proposed method, experiments on some images are performed.

• 한국수학사학회지
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• 제27권2호
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• pp.111-125
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• 2014

Jisuguimundo is an inimitable magic hexagon devised by Choi Seok-Jeong, who was the author of GuSuRyak as well as a prime minister in Joseon dynasty. Jisuguimundo, recorded in GuSuRyak, is also known as Hexagonal Tortoise Problem (HTP) because its nine hexagons resemble a tortoise shell. We call the sum of numbers in a hexagon in Jisuguimundo a magic sum, and show that the magic sum of hexagonal tortoise problem of order 2 varies 40 through 62 exactly and that of hexagonal tortoise problem of order 3 varies 77 through 109 exactly. We also find all of the possible solutions for hexagonal tortoise problem of oder 2.

• 대한수학회보
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• 제56권4호
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• pp.815-827
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• 2019

It is well known that the denominator of the Dedekind sum s(c, d) divides 2 gcd(d, 3)d and that no smaller denominator independent of c can be expected. In contrast, here we prove that we usually get a smaller denominator in S(H, d), the sum of the s(c, d)'s over all the c's in a subgroup H of order n > 1 in the multiplicative group $(\mathbb{Z}/d\mathbb{Z})^*$. First, we prove that for p > 3 a prime, the sum 2S(H, p) is a rational integer of the same parity as (p-1)/2. We give an application of this result to upper bounds on relative class numbers of imaginary abelian number fields of prime conductor. Finally, we give a general result on the denominator of S(H, d) for non necessarily prime d's. We show that its denominator is a divisor of some explicit divisor of 2d gcd(d, 3).

• 자원ㆍ환경경제연구
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• 제9권3호
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• pp.461-487
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• 2000

Kang et al. (1999) computed a composite environmental index in Korea by practicing the survey for environmental experts. They used the weighted sum form among feasible aggregation forms. In this study, we carry out the survey for both experts and non-experts to see the degree of differences of the weights for nine types of environmental problems between two groups. In addition, we apply different aggregation forms such as linear sum, weighted sum, root-sum-power, root-mean-square forms and compare these four outcomes. We found no significant discrepancy in the trends of composite indices. In case we rely on the weights provided by the experts, the composite index, on average, has been increased annually by about 7.2% over the 1986~1997 period, which informs us that overall environmental quality in 1997 has been worse than in 1986 by about 1.8 times.