• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권1호
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• pp.177-193
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• 2010

본 연구는 고등학교 통계 영역의 확률분포에 제시되어 있는 정규분포를 이항분포에서 정규분포로의 근사, 정규분포곡선의 탐구, Monte Carlo 방법에 의한 정규분포곡선의 넓이 탐구, 정규분포곡선의 선형변환, 그리고 여러 형태의 정규분포곡선 탐구 등의 내용을 중심으로 CAS 계산기를 활용하여 탐구해보고자 한다. CAS 계산기의 도구적 기능인 사소화, 실험, 시각화, 집중의 측면에서 볼 때 지필로서는 교육과정에 제시된 확률분포의 목표를 달성하기 불가능하다고 판단된다. 따라서 본 연구에서는 CAS 계산기를 활용하여 정규분포곡선의 다양한 성질을 탐구하고 이러한 과정과 결과로부터 정규분포곡선에 대한 교수학적 시사점을 도출하고자 한다.

• Geomechanics and Engineering
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• 제12권2호
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• pp.185-195
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• 2017

With the rapid development of urban underground traffic, the study of soil deformation induced by subway tunnel construction and its settlement prediction are gradually of general concern in engineering circles. The law of soil displacement caused by shield tunnel construction of adjacent buildings is analyzed in this paper. The author holds that ground surface settlement based on the Gauss curve or Peck formula induced by tunnel excavation of adjacent buildings is not reasonable. Integrating existing research accomplishments, the paper proposed that surface settlement presents cork distribution curve characters, skewed distribution curve characteristics and normal distribution curve characteristics when the tunnel is respectively under buildings, within the scope of the disturbance and outside the scope of the disturbance. Calculation formulas and parameters on cork distribution curve and skewed distribution curve were put forward. The numerical simulation, experimental comparison and model test analysis show that it is reasonable for surface settlement to present cork distribution curve characters, skewed distribution curve characteristics and normal distribution curve characteristics within a certain range. The research findings can be used to make effective prediction of ground surface settlement caused by tunnel construction of adjacent buildings, and to provide theoretical guidance for the design and shield tunnelling.

• 대한기계학회논문집A
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• 제32권9호
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• pp.707-712
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• 2008

The fatigue characteristics of a material or a structure are generally derived from fatigue tests of standard specimens. However, test results of standard specimens are different from those of real structures or components. Therefore, to calculate more accurate fatigue life, the geometrical effect and surface condition must be considered by comparing test results of standard specimens with those of real structures or components. Thus the object of this paper is to evaluate the fatigue characteristics of a real waterwork pipe. Also, to evaluate fatigue characteristic based on life distribution, the statistical fatigue characteristics were analyzed by the normal distribution and related data of P-S-N curve.

• Computers and Concrete
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• 제15권2호
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• pp.199-213
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• 2015

The residual fracture toughness of post-fire normal-strength concrete subjected up to $600^{\circ}C$ is considered by the wedge splitting test. The initial fracture toughness $K_I^{ini}$ and the critical fracture toughness $K_I^{un}$ could be calculated experimentally. Their difference is donated as the cohesive fracture toughness $K_I^c$ which is caused by the distribution of cohesive stress on the fracture process zone. A comparative study on determining the residual fracture toughness associated with three bi-linear functions of the cohesive stress distribution, i.e. Peterson's softening curve, CEB-FIP Model 1990 softening curve and Xu's softening curve, using an analytical method is presented. It shows that different softening curves have no significant influence on the fracture toughness. Meanwhile, comparisons between the experimental and the analytical calculated critical fracture toughness values further prove the validation of the double-K fracture model to the post-fire concrete specimens.

• 한국수학사학회지
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• 제13권1호
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• pp.1-14
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• 2000

The first part of this thesis discusses the Pearson's Curve Family which gives $\beta$distribution, $\Gamma$-distribution, $X^2$-distribution and t-distribution. The second part of this thesis gives some brief process of calculations for normal distribution density and t-distribution density by the 7-th type Curve of Pearson's Curve Family. Finally, a conclusion arrives that Student(Gosset) could not find out his famous 'Student's t-distribution' without his attending of 'Pearson's Differential Equation' class taught by Pearson himself when he was a senior student. However, if he had got a professorship at the Pearson Statistics Laboratory, the University of London, then he could not have found 'Student's t-distribution' for small sampling technique of modern statistics.

• 한국군사과학기술학회지
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• 제17권2호
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• pp.204-212
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• 2014

The purpose of this paper is to investigate the effects of calibration rounds on the statistical distribution of the muzzle velocity in acceptance test of propelling charge. It is shown that the normal distribution fits best among statistical distributions from goodness-of fit test. The 3p-Weibull distribution is also acceptable because the shape of the probability density function curve is similar to that of normal distribution and it also has near zero skewness value. Muzzle velocities of test rounds uncompensated by calibration rounds showed high variation and had comparatively higher skewness. Because the skewness of normal distribution is defined to be zero, calibration rounds make the normality of data higher.

• Korean Journal of Mathematics
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• 제32권2호
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• pp.259-284
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• 2024

In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear combination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

• 응용통계연구
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• 제25권5호
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• pp.803-811
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• 2012

For credit evaluation models, we extend the study of discriminatory power based on AUC obtained from a ROC curve when the number of defaults is small and distribution functions of the defaults and non-defaults are normal distributions. Since distribution functions do not satisfy normality in real world, the distribution functions of the defaults and non-defaults are assumed as normal mixture distributions based on results that the normal mixture could be better fitted than other distribution estimation methods for non-normal data. By using several AUC statistics, the discriminatory power under such a circumstance is explored and compared with those of normal distributions.

• Communications for Statistical Applications and Methods
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• 제19권4호
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• pp.629-638
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• 2012

We propose some methods to obtain optimal thresholds and classification functions by using various cutoff criterion based on the bivariate ROC curve that represents bivariate cumulative distribution functions. The false positive rate and false negative rate are calculated with these classification functions for bivariate normal distributions.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 춘계학술대회 논문집
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• pp.1691-1694
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• 2005

The fatigue characteristic of a material or a structure is derived from fatigue tests of standard specimens. However test results of standard specimens are very different from those of real structures or components. Therefore, to calculate more accurate fatigue life, the geometrical effect and surface condition must be considered by comparing test results of standard specimens with those of real structures or components. Thus the object of this paper is to evaluate the fatigue characteristic of a real waterwork pipe by conducting fatigue tests with standard specimens and non-standard(plate-shaped) specimens of base metal and weld metal. Also, to evaluate fatigue characteristic based on life distribution, statistical fatigue characteristic was analyzed by the normal distribution and related data of P-S-N curve.