• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.49-60
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• 2004

In this paper, when the observations are distributed as inverse gaussian, we developed the noninformative priors for ratio of the parameters of inverse gaussian distribution. We developed the first order matching prior and proved that the second order matching prior does not exist. It turns out that one-at-a-time reference prior satisfies a first order matching criterion. Some simulation study is performed.

• Science of Emotion and Sensibility
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• v.17 no.2
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• pp.63-76
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• 2014

Although most behavioral reaction times (RTs) for cognitive tasks exhibit positively skewed distributions, the majority of studies primarily rely on a measure of central tendency (e.g. mean) which can cause misinterpretations of data's underlying property. The purpose of current study is to introduce procedures for describing characteristics of RT distributions, thereby effectively examine the influence of experimental manipulations. On the basis of assumption that RT distribution can be represented as a convolution of Gaussian and exponential variables, we fitted the ex-Gaussian function under a maximum-likelihood method. The ex-Gaussian function provides quantitative parameters of distributional properties and the probability density functions. Here we exemplified distributional analysis by using empirical RT data from two conventional visual search tasks, and attempted theoretical interpretation for setsize effect leading proportional mean RT delays. We believe that distributional RT analysis with a mathematical function beyond the central tendency estimates could provide insights into various theoretical and individual difference studies.

• Composites Research
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• v.29 no.5
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• pp.299-305
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• 2016

This paper presents a method to detect the fiber property variation of laminated CFRP plates using the bivariate Gaussian distribution function. Five unknown parameters are considered to determine the fiber damage distribution, which is a modified form of the bivariate Gaussian distribution function. To solve the inverse problem using the combined computational method, this study uses several natural frequencies and mode shapes in a structure as the measured data. The numerical examples show that the proposed technique is a feasible and practical method which can prove the location of a damaged region as well as inspect the distribution of deteriorated stiffness of CFRP plates for different fiber angles and layup sequences.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1271-1284
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• 2011

The entropy-based test of fit for the inverse Gaussian distribution presented by Mudholkar and Tian(2002) can only be applied to the composite hypothesis that a sample is drawn from an inverse Gaussian distribution with both the location and scale parameters unknown. In application, however, a researcher may want a test of fit either for an inverse Gaussian distribution with one parameter known or for an inverse Gaussian distribution with both the two partameters known. In this paper, we introduce tests of fit for the inverse Gaussian distribution based on the Kullback-Leibler information as an extension of the entropy-based test. A window size should be chosen to implement the proposed tests. By means of Monte Carlo simulations, window sizes are determined for a wide range of sample sizes and the corresponding critical values of the test statistics are estimated. The results of power analysis for various alternatives report that the Kullback-Leibler information-based goodness-of-fit tests have good power.

• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.37-47
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• 2013

A Q-Q plot is an effective and convenient graphical method to assess a distributional assumption of data. The primary step in the construction of a Q-Q plot is to obtain a closed-form expression to represent the relation between observed quantiles and theoretical quantiles to be plotted in order that the points fall near the line y = a + bx. In this paper, we introduce a Q-Q plot to assess goodness-of-fit for inverse Gaussian distribution. The procedure is based on the distributional result that a transformed random variable $Y={\mid}\sqrt{\lambda}(X-{\mu})/{\mu}\sqrt{X}{\mid}$ follows a half-normal distribution with mean 0 and variance 1 when a random variable X has an inverse Gaussian distribution with location parameter ${\mu}$ and scale parameter ${\lambda}$. Simulations are performed to provide a guideline to interpret the pattern of points on the proposed inverse Gaussian Q-Q plot. An illustrative example is provided to show the usefulness of the inverse Gaussian Q-Q plot.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.383-391
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• 2011

This paper presents a modified entropy-based test of fit for the inverse Gaussian distribution. The test is based on the entropy difference of the unknown data-generating distribution and the inverse Gaussian distribution. The entropy difference estimator used as the test statistic is obtained by employing Vasicek's sample entropy as an entropy estimator for the data-generating distribution and the uniformly minimum variance unbiased estimator as an entropy estimator for the inverse Gaussian distribution. The critical values of the test statistic empirically determined are provided in a tabular form. Monte Carlo simulations are performed to compare the proposed test with the previous entropy-based test in terms of power.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.04a
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• pp.82-85
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• 2003

강원도 춘천시 신북읍 유포리 연구지역의 지하수의 NO$_3$-N 2차원 공간 분포를 정의하기 위하여 지구통계학적 해석 방법인 sequential Gaussian simulation(SGS)을 이용하였다. 원자료의 공간적 clustering을 제거하기 위하여 cell declustering을 수행한 후 normal score 변환을 거친 후 variogram 분석과 모델링을 수행하였다. Exponential, gaussian, spherical variogram model에 대한 각각의 nugget, range, sill을 정의하여 SGS에 이용하였다. SGS에 의해 도출된 결과들은 모두 동일한 결과를 나타낸다. 또한 관측 자료의 분포와 주 오염원의 분포와 상응하는 모델링 결과를 나타내는 것으로 보아 SGS를 이용한 농촌지역 지하수내 NO$_3$-N의 공간적 오염 분포 영상화가 매우 유용하게 활용될 수 있을 것으로 판단된다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.5
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• pp.1143-1148
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• 2014

This paper has analyzed the change of subthreshold swing for doping distribution function of asymmetric double gate(DG) MOSFET. The basic factors to determine the characteristics of DGMOSFET are dimensions of channel, i.e. channel length and channel thickness, and doping distribution function. The doping distributions are determined by ion implantation used for channel doping, and follow Gaussian distribution function. Gaussian function has been used as carrier distribution in solving the Poisson's equation. Since the Gaussian function is exactly not symmetric for top and bottome gates, the subthreshold swings are greatly changed for channel length and thickness, and the voltages of top and bottom gates for asymmetric double gate MOSFET. The deviation of subthreshold swings has been investigated for parameters of Gaussian distribution function such as projected range and standard projected deviation in this paper. As a result, we know the subthreshold swing is greatly changed for doping profiles and bias voltage.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.741-752
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• 2016

Numerous studies have shown that normal inverse Gaussian (NIG) distribution adequately fits the empirical return distribution of financial securities. The estimation of parameters can also be done relatively easily, which makes the NIG distribution more useful in financial markets. The maximum likelihood estimation and the method of moments estimation are easy to implement; however, we may encounter a problem in practice when a relationship among the moments is violated. In this paper, we investigate this problem in the parameter estimation and try to find a simple solution through simulations. We examine the effect of our adjusted estimation method with real data: daily log returns of KOSPI, S&P500, FTSE and HANG SENG. We also checked the performance of our method by computing the value at risk of daily log return data. The results show that our method improves the stability of parameter estimation, while it retains a comparable performance in goodness-of-fit.

• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.203-213
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• 2017

We study estimation and inference of joint conditional distributions of bivariate longitudinal outcomes using regression models and copulas. We consider a class of time-varying transformation models and combine the two marginal models using Gaussian copulas to estimate the joint models. Our models and estimation method can be applied in many situations where the conditional mean-based models are inadequate. Gaussian copulas combined with time-varying transformation models may allow convenient and easy-to-interpret modeling for the joint conditional distributions for bivariate longitudinal data. We apply our method to an epidemiological study of repeatedly measured bivariate cholesterol data.