• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1191-1200
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under two non-normal distributions.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.473-481
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent. Kim(2001) proposed a modified Shapiro-Wilk's test statistic based on the ratio of tow asymptotically efficient estimates of scale. In this paper, we study the asymptotic behavior of the statistic using the approximation of the quantile process by a sequence of Brownian bridges and represent the limit null distribution as an integral of a Brownian bridge.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.203-212
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under two non-normal distributions.

• Steel and Composite Structures
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• v.24 no.3
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• pp.369-382
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• 2017

This study investigates the reliability of the performance levels of moment resisting steel frames subjected to lateral loads such as wind and earthquake. The reliability assessment has been performed with respect to three performance levels: serviceability, damageability, and ultimate limit states. A four-story moment resisting frame is used as a typical example. In the reliability assessment the uncertainties in the loadings and in the capacity of the frame have been considered. The wind and earthquake loads are assumed to have lognormal distribution, and the frame resistance is assumed to have a normal distribution. In order to obtain an appropriate limit state function a linear relation between the loading and the deflection is formed. For the reliability analysis an algorithm has been developed for determination of limit state functions and iterations of the first order reliability method (FORM) procedure. By the method presented herein the multivariable analysis of a complicated reliability problem is reduced to an S-R problem. The procedure for iterations has been tested by a known problem for the purpose of avoiding convergence problems. The reliability indices for many cases have been obtained and also the effects of the coefficient of variation of load and resistance have been investigated.

• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.155-162
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• 2003

A tandem network in which all nodes have the same load is considered. We derive bounds on the probability that the total population of the tandem network exceeds a large value by using its relation to the stationary distribution. These bounds imply a stronger asymptotic limit than that in the large deviation theory.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.715-723
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• 2003

A tandem network in which all nodes have the same load is considered. We derive bounds on the probability that the total population of the tandem network exceeds a large value by using its relation to the stationary distribution. These bounds imply a stronger asymptotic limit than that in the large deviation theory.

• The Korean Journal of Ecology
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• v.17 no.4
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• pp.513-521
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• 1994

Distribution patern of 30 species that are occurring predominantly in the mantle communities (Mantelgesellschaften) in South Korea was studied. The study was arried out by geographic and bioclimatic analysis on 368 releves obtained from the Zurich-Montpellier School's method, which involves direct analysis on the latitude, altitude, annual mean temperature and the lowest temperature of the site. Rosa multiflora and Pueraria thunbergiana which are regarded as repersentative pioneer species to the mantle community has the highest frequency, 70.1% and 60.3%, respectively. Three distribution patterns were recognized, i.e. northern type, central type and southern type, and each type was characterized by horizontal and altitudinal amplitude. Their concetrate distribution ranges on the annual mean temperature were 8~11℃, 9~12℃ and 10~13℃, respectively. It was recognized that tendencies of overlapping and continuous distribution pattern of the types and species exist. Geographically, the souther limit f the northern type is 35.5。N and the northern limit of the southern type 37.0。N. The central type is located at an coincided with the previous study in which cool-temperate forests were synchorologically indentified into northern/altimontane, certral/montane and southern/submontane type. The subsidiary knowledges from this study will provide practical information on the constructuin of the fence plant community for environmental conservation.

• Journal of the Korea Society of Computer and Information
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• v.21 no.7
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• pp.85-92
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• 2016

The law of large numbers, central limit theorem, and connection among binomial distribution, normal distribution, and statistical estimation require dynamics of continuous visualization for students' better understanding of the concepts. During this visualization process, the differences and similarities between statistical probability and mathematical probability that students should observe need to be provided with the intermediate steps in the converging process. We propose a visualization method that can integrate intermediate processes and results through Excel. In this process, students' experiences with dynamic visualization help them to perceive that the results are continuously changed and extracted from multiple situations. Considering modeling as a key process, we developed a classroom exercise using Excel to estimate the population mean and standard deviation by using a sample mean computed from a collection of data out of the population through sampling.

• Nuclear Engineering and Technology
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• v.51 no.5
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• pp.1261-1271
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• 2019

Droplet size and distribution are important parameters determining venturi scrubber performance. In this paper, we proposed physical models for a maximum stable droplet size prediction and upper limit log-normal (ULLN) distribution parameters. For the proposed maximum stable droplet size prediction model, a Eulerian-Lagrangian framework and a Reitz-Diwakar breakup model are solved simultaneously using CFD calculations to reflect the effect of multistage breakup and droplet acceleration. Then, two ULLN distribution parameters are suggested through best fitting the previously published experimental data. Results show that the proposed approach provides better predictions of maximum stable droplet diameter and Sauter mean diameter compared to existing simple empirical correlations including Boll, Nukiyama and Tanasawa. For more practical purpose, we developed the simple, one dimensional (1-D) calculation of Sauter mean diameter.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.295-304
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• 2015

This paper considers the problem of estimation of the Hurst parameter H ${\in}$ (1/2, 1) from longitudinal data with the error term of a fractional Brownian motion with Hurst parameter H that gives the amount of the long memory of its increment. We provide a new estimator of Hurst parameter H using a two scale sampling method based on $A{\ddot{i}}t$-Sahalia and Jacod (2009). Asymptotic behaviors (consistent and central limit theorem) of the proposed estimator will be investigated. For the proof of a central limit theorem, we use recent results on necessary and sufficient conditions for multi-dimensional vectors of multiple stochastic integrals to converges in distribution to multivariate normal distribution studied by Nourdin et al. (2010), Nualart and Ortiz-Latorre (2008), and Peccati and Tudor (2005).