• Geomechanics and Engineering
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• v.12 no.2
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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.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.169-174
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• 2013

The ROC curve is drawn with two conditional cumulative distribution functions (or survival functions) of the univariate random variable. In this work, we consider joint cumulative distribution functions of k random variables, and suggest a ROC curve for multivariate random variables. With regard to the values on the line, which passes through two mean vectors of dichotomous states, a joint cumulative distribution function can be regarded as a function of the univariate variable. After this function is modified to satisfy the properties of the cumulative distribution function, a ROC curve might be derived; moreover, some illustrative examples are demonstrated.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.249-256
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• 2001

We shall derive the MLE and UMVUE of Lorenz Curve and Gini Index in a Pareto distribution with the pdf(1.1) and their variances. And compare mean square errors(MSE) of the MLE and UMVUE of the Lorenz Curve and Gini Index in a Pareto distribution with pdf(1.1).

• Communications of Mathematical Education
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• v.24 no.1
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• pp.177-193
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• 2010

The purpose of this study is to explore normal distribution in probability distributions of the area of statistics in high school mathematics. To do this these contents such as approximation of normal distribution from binomial distribution, investigation of normal distribution curve and the area under its curve through the method of Monte Carlo, linear transformations of normal distribution curve, and various types of normal distribution curves are explored with CAS calculator. It will not be ablt to be attained for the objectives suggested the area of probability distribution in a paper-and-pencil classroom environment from the perspectives of tools of CAS calculator such as trivialization, experimentation, visualization, and concentration. Thus, this study is to explore various properties of normal distribution curve with CAS calculator and derive from pedagogical implications of teaching and learning normal distribution curve.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.2B no.4
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• pp.168-173
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• 2002

A new identification algorithm for the Preisach model is presented. The algorithm treats the identification procedure of the Preisach model as an inverse problem where the independent variables are parameters of the distribution function and the objective function is constructed using only the initial magnetization curve or only tile major loop of the hysteresis curve as well as the whole reversal curves. To parameterize the distribution function, the Bezier spline and Gaussian function are used for the coercive and interaction fields axes, respectively. The presented algorithm is applied to the ferrite permanent magnets, and the distribution functions are correctly found from the major loop of the hysteresis curve or the initial magnetization curve.

• Journal for History of Mathematics
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• v.13 no.1
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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.

• The Korean Journal of Applied Statistics
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• v.27 no.3
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• pp.445-459
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• 2014

As a certain job is repeatedly done by a worker, the outcome comparative to the effort to complete the job gets more remarkable. The outcome may be the time required and fraction defective. This phenomenon is referred to a learning-curve effect. We focus on the parametric modeling of the learning-curve effects on count data using a logistic cumulative distribution function and some probability mass functions such as a Poisson and negative binomial. We conduct various simulation scenarios to clarify the characteristics of the proposed model. We also consider a real application to compare the two discrete-type distribution functions.

• Journal of the Korean Ceramic Society
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• v.33 no.5
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• pp.583-589
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• 1996

In this study a new analytical model which can describe the relationship between the bridging stress and microstructure has beenproposed in order to investigate the microstructural effect on the R-curve behavior in polycrystalline aluminas since the R-curve can be derived via the bridging stress function. In the currently developed model function the distribution of grain size is considered as a microstructural factor in modeling of bridging stress function and thus the bridging stress function including three constants PM, n, and Cx, can be established analytically and quantitatively. The results indicate that the n value is closely related to the grain size distribution thereby providing a reliability of the current model for the bridging stress analysis. Thus this model which explains the correlation of the bridging stress distribution and microstructual parame-ters is useful for the systematic interpretation of microfracture mechanism including the R-curve behavior in polycrystalline aluminas.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.11
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• pp.518-524
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• 2005

This paper presents an analytical method for the reliability evaluation of distribution system, including the distributed generations. Unlike the large sized generations of transmission system, the distributed generations have complexities in analyzing and determining the operation. In the process of evaluate reliability, it can be shown that the analytical method is simpler than the Monte-Carlo simulation and the method using Load Duration Curve model is more accurate than that using peak load model. The modeling of distributed generation to analysis distribution system reliability using LDC is proposed in this Paper, and is compared with the MCS method as a result of case studies.

• Journal of the Korean Statistical Society
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• v.35 no.3
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• pp.305-316
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• 2006

Absolute Lorenz curve plays an important role for measuring absolute income inequality. Properties of absolute Lorenz curve are listed. Asymptotically distribution free and consistent tests have been proposed for comparing two absolute Lorenz curves in the whole interval [P1, P2] where 0 < P1 < P2 < 1. Absolute Lorenz ordering has been discussed for some distributions.