• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.223-232
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• 2002

The present paper develops a test of the multivariate normality based on nonlinear transformations and the likelihood function. For checking the normality, we test the shape parameter which indexes the family of transformations. A score test and a parametric bootstrap test are used to evaluate the discrepancy between the data and a multivariate normal distribution. In order to compare the performance of our test with the existing tests, a simulation study was carried out for several situations where nuisance parameters have to be estimated. The results showed that the proposed method is superior to the existing methods.

• Journal of the Korean School Mathematics Society
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• v.23 no.4
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• pp.427-448
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• 2020

The purpose of this study is to confirm the MKT(Mathematical Knowledge for Teaching) of the pre-service mathematics teachers on the normal distribution through the comparative analysis between the sub-elements of the MKT. In addition, it is to examine the factors that cause the difference of the subjects' MKT. To accomplish this, by the subject of 24 secondary pre-service mathematics teachers, in this study the test items of the MKT on the normal distribution were developed and data were collected and analyzed. As a result of the analysis of the MKT test sheet, the CCK(Common Content Knowledge) of the preparatory mathematics teacher was confirmed as a high score, whereas the SCK(Specialized Content Knowledge) and KCS(Knowledge of Content and Students) were confirmed as low scores. In addition, through these results, it could be confirmed that the difference in MKT of preparatory mathematicians occurred.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.1
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• pp.88-93
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• 1994

This study is concerned with an analytic derivation of the probability density function applicable for wave heights in finite water depth using two different methods. As the first method of the study, a probability density function is developed by applying a series of polynomials which is orthogonal with respect to Rayleigh probability density function. The newly derived probability density function is compared with the histogram constructed from wave data obtained in finite water depth which indicate strong non-Gaussian characteristics. Although the probability density represents the histogram very well. it has negative density at large values. Although the magnitude of the negative density is small. it negates the use of the distribution function fer estimating extreme values. As the second method of the study, a probability density function of wave height is developed by applying the maximum entropy method. The probability density function thusly derived agrees very well with the wave height distribution in shallow water, and appears to be useful in estimating extreme values and statistical properties of wave heights in finite water depth. However, a functional relationship between the probability distribution and the non-Gaussian characteristics of the data cannot be obtained by applying the maximum entropy method.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.11-23
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• 1996

본 연구에서는 선형회귀분석에서 Hadi와 Simonoff의 다중이상점 식별방법을 수정하여 새로운 알고리즘을 제시하였다. Hadi와 Simonoff의 알고리즘 첫 단계에서 이상점일 가능성이 없는 점들의 집합을 추출할 때 가장효과와 편승효과에 영향을 받을 수 있음으로, 이 첫 단계를 수정하였다. 우리는 잔차가 일정한 분산을 갖는 정규분포에 다르다는 가정하에서 잔차의 신뢰구간을 생각하고, 이 구간안에서 잔차의 MAD가 최소인 새로운 모형을 탐색하고, 이를 이상점일 가능성이 없는 점들의 집합을 추출하는데 일용하는 새로운 알로리즘을 제시하였다. 제시된 방법은 실제자료에서 다른 방법에 비해 효율적으로 이상점을 식별할 수 있었다.

• Journal of the Korean Geophysical Society
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• v.3 no.3
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• pp.161-174
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• 2000

Bayesian inversion is a stable approach to infer the subsurface structure with the limited data from geophysical explorations. In geophysical inverse process, due to the finite and discrete characteristics of field data and modeling process, some uncertainties are inherent and therefore probabilistic approach to the geophysical inversion is required. Bayesian framework provides theoretical base for the confidency and uncertainty analysis for the inference. However, most of the Bayesian inversion require the integration process of high dimension, so massive calculations like a Monte Carlo integration is demanded to solve it. This method, though, seemed suitable to apply to the geophysical problems which have the characteristics of highly non-linearity, we are faced to meet the promptness and convenience in field process. In this study, by the Gaussian approximation for the observed data and a priori information, fast Bayesian inversion scheme is developed and applied to the model problem with electric well logging and dipole-dipole resistivity data. Each covariance matrices are induced by geostatistical method and optimization technique resulted in maximum a posteriori information. Especially a priori information is evaluated by the cross-validation technique. And the uncertainty analysis was performed to interpret the resistivity structure by simulation of a posteriori covariance matrix.

• Journal of Korean Society for Atmospheric Environment
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• v.7 no.3
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• pp.180-188
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• 1991

기후변화를 나타내는 연구 결과들은 기온이나 강수량을 대상으로 하여 두 기간 평균치의 비교, 5년 이동평균치의 圖示, 회귀분석 등의 방법들을 사용하여 발표되지만 대부분의 경우 밑바탕이 되는 모집단의 통계적 특성을 엄격히 검토하지 않는 정성적인 분석인 경우가 많다. 서울, 부산, 인천, 목포 등 4개 지점의 80년 동안의 연강수량과 연평균기온자료를 분석한 결과 기온은 정규분포를 나타내므로 전통적인 t-검정과 회귀분석을 적용할 수 있다. t-검정 결과 두 기간(1920 $sim$ 1949, 1961 ~ 1990)은 연평균기온에서 0.3$^{\circ}$C에서 $0.8^{\circ}$C의 의의있는 차이를 보였다. 최근 30년의 연평균기온자료를 회귀분석한 결과 1년에 $0.02^{\circ}$C의 증가경향을 나타내었다. 연강수량은 정적인 왜곡도를 보이므로 정규분포를 가정하는 母數的 통계분석을 적용해서는 안되며 비모수적 통계분석법을 적용해야 한다. 연강수량의 분석에는 t-검정에 상응하는 Mann-Whitney 검정을 적용해 본 결과 두 기간(1920 ~ 1949, 1961 ~ 1990)의 평균은 통계적으로 의의있는 차이가 없었다. 회귀분석에 상응하는 Mann's 검정과 이 연구에서 새로이 제안된 Median Slope Change Estimator를 적용해 본 결과 역시 통계적으로 의의있는 변화가 없었다. Median Slope Change Estimator는 비모수적 통계치로서 회귀분석의 기울기에 해당하는 연변화를 나타낼 수 있는데 분석하려는 자료의 정규분포성을 요구하지 않으며 異常點(outlier) 영향에 덜 민감하다는 장점이 있으므로 주목하여 연구할 만한 가치가 있다.^{\circ}$~40$^{\circ}$ 구간에서는 ${\sigma}_c$와 I$_{sa}$, 40$^{\circ}$~90$^{\circ}$ 구간에서는 ${\sigma}_c$와 I$_{sd}$가 각각 양호한 상관관계를 보여준다. 또한 상관비(K=${\sigma}_c$/I$_s$)는 약 13정도로서 일반적으로 적용되는 비, 24와 상당한 차이가 있다. 이러한 현상은 호상편마암의 구조적 및 역학적 이방성 특성으로 인한 결과라고 판단된다. 한편 맥암류에서 K가 약 23정도로서 일반적인 비 24에 상당히 접근한다. 따라서, 이방성 구조가 뚜렷한 암석에서 상관비 24는 항상 적용할 수는 없으며 일축압축강도시험과 병행 실시하여 적용하는 것이 바람직하다.다. 한편, 감작감염후 77일과 도전감염후 7일의 시점에 있어서 sRBC에 대한 면역능에 미치는 영향은 전자의 양상과 비슷하였는데 대조에 비하여 지연형 과민반응과 로제트 형성능이 현저하게 저하되었다. 이 시점에 있어서의 유충회수율은 대조가 10.5% 이었는데 비하여 8.3%이었다.e also compared for the cases of Kim et al, which again gives promising agreement.면적 306~453$\textrm{cm}^2$, 유색계의 경우 수당면적 340~453$\textrm{cm}^2$ 일 때 경제능력을 제대로 발휘할 수 있고 경제성이 있는 것으로 나타났다. 첨가구가 높은 경향이 있었다8.4%. 79.7% 그리고 80.2%였다.

• Journal of the Korean Data and Information Science Society
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• v.28 no.5
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• pp.1077-1085
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• 2017

In this study, we have found the major factors which affect Korean women's wage analysing the data provided by 2015 Korea Labor Panel Survey (KLIPS). In general, wage data is difficult to analyze because random sampling is infeasible. Heckman sample selection model is the most widely used method for analysing the data with sample selection. Heckman proposed two kinds of selection models: the one is the model with maximum likelihood method and the other is the Heckman two stage model. Heckman two stage model is known to be robust to the normal assumption of bivariate error terms. Recently, Marchenko and Genton (2012) proposed the Heckman selectiont model which generalizes the Heckman two stage model and concluded that Heckman selection-t model is more robust to the error assumptions. Employing the two models, we carried out the analysis of the data and we compared those results.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2007.11a
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• pp.204-208
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• 2007

보험요율 및 정책 결정의 기본이 되는 파산 확률은 계산이 매우 복잡하여 보통 근사적인 방법을 사용하게 된다. 윤복식(2007)에서는 다양한 상황에서 정확하게 파산확률을 계산할 수 있는 방법이 GPH 분포에 기초하여 제안된 바 있다. 본 연구에서는 이 방법의 타당성을 다양한 실험을 통해 검증하고. 기존의 근사적 방법들과의 비교하는 것이 목적이다. 실험을 통해 이 방법이 일상적인 상황에서 뿐 아니라 클레임 분포가 비정규적인 대재해 상황에서도 정확하게 파산확률을 계산해 주는 것을 관찰할 수 있었고, 계산시간 또한 도 매우 짧아서 실용성을 겸비함을 확인할 수 있었다 또한 이 결과를 근거로, 기초적인 관측 자료만 입력하면 중간에 분포모델 설정단계를 거치지 않고 바로 분석 결과를 얻는 접근법이 제안된다.

• Environmental and Resource Economics Review
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• v.16 no.4
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• pp.947-978
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• 2007

In this paper, we investigated a Value-at-Risk approach to the volatility of two crude oil markets (Brent and Dubai). We also assessed the performance of various VaR models (RiskMetrics, GARCH, IGARCH and FIGARCH models) with the normal and skewed Student-t distribution innovations. The FIGARCH model outperforms the GARCH and IGARCH models in capturing the long memory property in the volatility of crude oil markets returns. This implies that the long memory property is prevalent in the volatility of crude oil returns. In addition, from the results of VaR analysis, the FIGARCH model with the skewed Student-t distribution innovation predicts critical loss more accurately than other models with the normal distribution innovation for both long and short positions. This finding indicates that the skewed Student-t distribution innovation is better for modeling the skewness and excess kurtosis in the distribution of crude oil returns. Overall, these findings might improve the measurement of the dynamics of crude oil prices and provide an accurate estimation of VaR for buyers and sellers in crude oil markets.

• Journal of the Korea Concrete Institute
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• v.23 no.4
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• pp.421-430
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• 2011

As a fundamental study to introduce the reliability-based design code, a statistical study is conducted for the material strength data collected from domestic construction sites. In order to develop a rational design code based on statistics and reliability theory, it is essential to obtain the statistical properties of material strength. Material strength data for concrete, reinforcing bars, and prestressing strands which are used in domestic construction sites are collected and statistically analyzed. Then, the statistical properties are compared with those used in the process of the reliability-based calibration of internationally leading design codes. The statistical properties of the domestic data are such that the bias factor is relatively uniform between 1.13 and 1.20 and the coefficient of variation is below 0.10. Reinforcing bar data show difference among different manufacturers but there is not much difference among re-bar diameters. In the case of tendons, which are high strength materials, both of the domestic and foreign data show smaller values of the bias factor and the coefficient of variation than those of concrete and re-bar. Statistical distribution of all the material strength can be properly assumed as normal, log-normal, or Gumbel distribution after analyzing the classified data by individual construction site and manufacturer rather than the mixed data obtained from different sources in order to express the individual distribution of each structure.