• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.847-856
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• 2013

In this paper, we deal with testing goodness-of-fit for normal distribution based on parametric and nonparametric entropy estimators. The minimum variance unbiased estimator for the entropy of the normal distribution is derived as a parametric entropy estimator to be used for the construction of a test statistic. For a nonparametric entropy estimator of a data-generating distribution under the alternative hypothesis sample entropy and its modifications are used. The critical values of the proposed tests are estimated by Monte Carlo simulations and presented in a tabular form. The performance of the proposed tests under some selected alternatives are investigated by means of simulations. The results report that the proposed tests have better power than the previous entropy-based test by Vasicek (1976). In applications, the new tests are expected to be used as a competitive tool for testing normality.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.357-371
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• 2007

For the time-to-failure data with competing risks, cumulative incidence functions (CIFs) are commonly estimated using nonparametric methods. If the cases of events due to the cause of primary interest are infrequent relative to other cause of failure, nonparametric methods may result in rather imprecise estimates for CIF. In such cases, Bryant et al. (2004) suggested to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimator. We represented the semiparametric cumulative incidence estimator and extended to the model of Weibull and log-normal distribution. We also conducted simulations to access the performance of the semiparametric cumulative incidence estimators and to investigate the impact of model misspecification in log-normal cause-specific hazard model.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.625-636
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• 2011

This paper proposes two parametric entropy estimators, the minimum variance unbiased estimator and the maximum likelihood estimator, for the lognormal distribution for a comparison of the properties of the two estimators. The variances of both estimators are derived. The influence of the bias of the maximum likelihood estimator on estimation is analytically revealed. The distributions of the proposed estimators obtained by the delta approximation method are also presented. Performance comparisons are made with the two estimators. The following observations are made from the results. The MSE efficacy of the minimum variance unbiased estimator appears consistently high and increases rapidly as the sample size and variance, n and ${\sigma}^2$, become simultaneously small. To conclude, the minimum variance unbiased estimator outperforms the maximum likelihood estimator.

• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.943-953
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• 2010

From a mixture distribution of the score random variable for credit evaluation, there are many methods of estimating optimal thresholds. Most the research news is based on the assumption of normal distributions. In this paper, we extend non-normal distributions such as Weibull, Logistic and Gamma distributions to estimate an optimal threshold by using a hypotheses test method and other methods maximizing the total accuracy and the true rate. The type I and II errors are obtained and compared with their sums. Finally we discuss their e ciency and derive conclusions for non-normal distributions.

• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.141-149
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• 2013

We present methods for studying the log-density ratio that enables the selection of the predictors and the form to be included in the logistic regression model. Under bivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of two predictors. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms. We also explore other conditions in which the crossproduct and quadratic terms are not needed in the logistic regression model.

• 한국해양학회지
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• v.28 no.2
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• pp.114-120
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• 1993

Numerical method of nonlinear regression was introduced to characterize grain-size distribution more effectively than using the traditional textural parameters. This technique proved critical particularly to multimodal size distributions, as exemplified by samples from Cheju strait continental shelf. Grain-size analysis of samples collected from the Cheju Strait continental shelf reveals that 86% of the grain-size distributions are multimodal. As multimodal grain-size distribution deviates from the statistical (log) normal distribution, the grain-size parameters traditionally used in sediment studies do not describe the distribution efficiently. Therefore, the use of grain-size curves into elementary normal component curves was used. Means and standard deviations of 387 decomposed normal components were decided by a decomposition method (nonlinear least square regression) from 167 size curves of the Cheju Strait sediments. The mean values of decomposed normal components show peaks at 1-3 phi and 8-9 phi size classes. The plot of mean values of the coarse fraction normal components on the map shows a characteristic and complex areal distribution. On the basis of the areal distribution of the mean values of the components and that of isopach of total Plenipotence sediment, the areal distribution of layers composing a transgressive sand of Late Plenipotence age were revealed.

• Journal of Radiation Protection and Research
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• v.31 no.1
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• pp.17-23
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• 2006

The purpose of this study is to provide the guidance necessary for making a selection of error distributions by analyzing influence of statistical distribution for a type of bioassay measurement error on the intake estimation. For this purpose, intakes were estimated using maximum likelihood method for cases that error distributions are normal and lognormal, and comparisons between two distributions for the estimated intakes were made. According to the results of this study, in case that measurement results for lung retention are somewhat greater than the limit of detection it appeared that distribution types have negligible influence on the results. Whereas in case of measurement results for the daily excretion rate, the results obtained from assumption of a lognormal distribution were 10 % higher than those obtained from assumption of a normal distribution. In view of these facts, in case where uncertainty component is governed by counting statistics it is considered that distribution type have no influence on intake estimation. Whereas in case where the others are predominant, it is concluded that it is clearly desirable to estimate the intake assuming a lognormal distribution.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.29-43
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• 2012

Financial data such as stock index returns and exchange rates have the properties of heavy tail and asymmetry compared to normal distribution. When we estimate VaR using the GARCH model (with the conditional return distribution of normal) it shows the tendency of the lower estimation and clustering in the losses over the estimated VaR. In this paper, we argue that this problem can be resolved through the adaptation of the unbounded Johnson distribution as that of the condition return. We also compare this model with the GARCH with the conditional return distribution of normal and student-t. Using the losses exceed the ex-ante VaR, estimates, we check the validity of the GARCH models through the failure proportion test and the clustering test. We nd that the GARCH model with conditional return distribution of unbounded Johnson provides an appropriate estimation of the VaR and does not occur the clustering of violations.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.1448-1452
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• 2010

최근 기상변동성 증가 및 기후변화 영향으로 수문순환과정이 과거와는 다른 양상으로 전개되고 있으며 전반적으로 극치사상의 빈도 및 강도의 증가현상이 지배적이다. 이러한 영향을 정량적으로 검토하기 위해서 경향성분석 방법 등이 도입되어 극치수문사상의 변동경향을 평가하는데 이용되고 있다. 대표적인 방법으로 선형회귀분석, Mann-Kendall 경향성 분석 등이 있으나 기본적인 가정(assumption)의 제약으로 극치수문자료 계열의 특성을 효과적으로 분석하는데 무리가 있다. 대표적이고 일반적으로 적용되는 선형회귀분석의 경우 자료가 정규분포(normal distribution)의 특성을 가질 때 유효한 방법으로서 극치수문자료와 같이 Heavy Tail를 가지는 분포특성을 표현하는 데는 무리가 따른다. 이밖에도 기존 선형회귀분석을 극치수문자료에 적용할 경우 추정된 결과를 수자원설계의 관심사항인 빈도해석 등에 직접적으로 연계시켜 해석할 수 없는 단점이 있다. 이는 자료계열의 분포특성을 정규분포로 가정하기 때문에 발생하는 문제로서 극치수문자료계열의 분포 특성을 반영할 수 있는 방법론의 개발이 필요하다. 본 연구에서는 이러한 점을 개선하기 위해서 극치분포(extreme distribution)를 선형회귀분석에 적용하는 비정상성빈도해석(nonstationary frequency analysis) 방법론의 개념을 제시하고자 한다. 비정상성빈도해석을 위해서 Bayesian 기법이 도입되며 Bayesian 기법의 특성상 관련변수들이 사후분포(posterior distribution)로 귀결되기 때문에 경향성에 대한 정량적이고 확률적인 분석이 가능한 장점이 있다. 본 연구를 통해 개발된 방법론은 국내외 주요 강수지점에 대해서 적용되며 경향성, 분포특성, 빈도별 강수량에 대한 체계적인 분석이 이루어진다.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 1998.10a
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• pp.807-813
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• 1998

이 논문에서는 로그정규분포에 대한 베이지안 모형선택방법을 제안한다. 일반적으로 , 모수에 대한 사전정보가 비정보적(noninformative)인 경우, 베이즈 요인(Bayes factor)은 결정할 수 없는 상수를 포함하는 것이 일반적이다. 이 경우, 베이즈 요인을 계산하기 위해 최근 활발히 연구중인 고유 베이즈 요인(Intrinsic Bayes factor)방법을 이용한다. 실제의 자료를 통해 로그정규분포의 적합도 검정에 대한 부분적 베이즈 요인을 계산한다.