• Proceedings of the Korea Water Resources Association Conference
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• 2017.05a
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• pp.4-4
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• 2017

수문자료의 빈도해석은 자료의 독립성(independence)와 정상성(stationarity)를 가정하여 이뤄진다. 그러나 관측 수문자료에서 비정상성 현상이 발생하고 있다는 사실이 관측되면서 수문자료에 대한 비정상성 빈도해석에 대한 필요성도 커지고 있다. 본 연구의 목적은 수문자료의 빈도해석에서 가장 널리 사용되고 있는 Gumbel 및 GEV 분포에 대한 비정상성 빈도해석 모형을 개발하는 것으로, 이를 위해 비정상성 Gumbel과 GEV 모형의 매개변수를 시간에 따라 변하는 형태로 정의하였다. 비정상성 Gumbel 및 GEV 모형의 정확도를 알아보기 위해 비정상성 모형과정상성 모형을 이용하여 Monte Carlo 모의실험을 수행하였다. 모의실험은 다양한 조건의 재현기간, 표본크기, 매개변수 조건을 고려하여 수행되었다. 그 결과 비정상성 모형의 오차는 비교적 표본크기가 클 때 가장 작은 것으로 나타났다. 또한 복잡한 매개변수의 조합을 가지는 비정상성 모형은 모두 동일한 경향성을 가질 때 가장 작은 오차를 보이는 것으로 나타났다. 비정상성 GEV 모형의 경우는 확률수문량 산정에 음(-)의 형상 매개변수가 큰 영향을 끼치는 것으로 나타났다. 또한 본 연구에서는 비정상성 조건에서 다양하게 존재하는 비정상성 모형 중 어떠한 모형이 주어진 자료에 대해 가장 적절한 모형인지 결정하기 위해 모의실험을 수행하였다. 널리 적용되고 있는 AIC, BIC, likelihood ratio test에 대해 정상성 및 비정상성 Gumbel 모형을 이용하여 모의실험을 수행한 결과, AIC가 비정상성 모형 중 적정 모형 선택에 가장 효과적인 것으로 나타났다. 개발된 비정상성 Gumbel 및 GEV 모형의 적용성을 알아보기 위해 우리나라 연최대강우 자료에 적용한 결과, 위치 매개변수에 시간항을 고려하는 Gumbel 모형이 최적모형으로 가장 많이 선택되는 것으로 나타났다. 따라서 현재 우리나라의 연최대강우자료 중 경향성이 나타나는 자료에 대해서는 위치 매개변수가 시간에 따라 변하는 특성이 가장 많이 나타나고 있는 것으로 판단된다.

• Journal of Korean Society of Forest Science
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• v.46 no.1
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• pp.29-43
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• 1980

The sampling methods selected for this area was (1) Simple random sampling (2) Systematic sampling and (3) Sub-sampling. For the calculation of the number of sampling plot, 10 % coefficient of variation was adapted. As a result, 57 plots each for simple random sampling and systematic sampling was calculated. In the sub-sampling method, however, total of 40 plots, which were consisted of 5 Blocks, secondary 4 major units and tertiary 2 minor units, were examined. The reuslts obtained are summarized as follows : 1. The rate of expected error was 9.24% for simple random sampling, 8.36% for systematic sampling and 7.54% for sub-sampling, respectively. Therefore, the sub-sampling was proved to be the most accurate method among the test. 2. The volume calculated by each sampling method was compared to the volume of all stand. The rate of expected error was also lowest in the sub-sampling (0.39%), followed by systematic sampling (4.18%) and simple random sampling (7.92%). 3. Comparing the various reuslts and analysis of these results, the sub-sampling was regarded as the most rapid and economical method because this method had not only the least number of plots but also the least expected error among the tested sampling methods Therefore the sub-sampling is proved to be an ideal sampling method for forest survey.

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.349-360
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• 2006

PROC MIXED in SAS can be utilized to make inferences on parameters in a mixed model by use of Restricted Maximum Likelihood Estimation Method or Maximum Likelihood Estimation Method which has more merits than ANOVA method. A regression model with unbalanced nested error structure that belongs to a mixed model is used to construct confidence intervals on variances among groups, within groups, and regression coefficients in the model. PROC MIXED is applied to three different sample sizes for simulation. As a result of the simulation study, PROC MIXED generates confidence intervals on parameters that maintain the stated confidence coefficient in a large sample size. However, it does not generate confidence intervals that maintain the stated confidence coefficient for variance components among groups and intercept in a small sample size.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.23-32
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• 2012

This paper deals with the bias and variance of regression coefficient estimators in a finite population. We derive approximate formulas for the bias, variance and mean square error of two estimators when we select a fixed-size inclusion probability proportional to the size sample and then estimate regression coefficients by the ordinary least square estimator as well as the weighted least square estimator based on the selected sample data. Necessary and sufficient conditions for the comparison of the two estimators in terms of variance and mean square error are suggested. In addition, a simple example is introduced to numerically compare the variance and mean square error of the two estimators.

• Proceedings of the Korean Association for Survey Research Conference
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• 2002.11a
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• pp.111-127
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• 2002

As the utilization of official statistics has been recently increased, the necessity of objective quality assessment also has been increased. Since mean square error(MSE) and response rate, which have been considered as representative quality indicators in the past, may have the limits of use, it has been demanded to develop new quality indicators which are able to reflect the various requirements of users. In this paper, regarding sample surveys conducted by governmental agencies, the flow of procedures in statistics production is analyzed using input-output of each procedure. As the result, how to identify and develop quality indicators for each procedure is discussed, with some instances of indicators. Finally, the quality index using the results of quality assessment would be calculated based on a weighting method by the size of deviation of statistical measures.

• Journal of Korean Society for Quality Management
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• v.9 no.1
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• pp.3-11
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• 1981

A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased (MVU) estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distirubtions are Weibull with unknown scale parameters and same known shape parameter. The asymptotic distribution of MVU estimate of system reliability in the model is obtained by using the standard asymptotic properties of the maximum likelihood estimate of system reliability and establishing their equivalence. Uniformly most accurate unbiased confidence intervals are also obtained for system reliability. Empirical comparison of the two estimates for small samples is studies by Monte Carlo simulation.

• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.105-117
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• 2004

In this paper, a new method is developed for estimating the mean of a population which has a linear trend. This method involves drawing a sample by the modified systematic sampling, and then estimating the population mean with an adjusted estimator, not with the sample mean itself. We use the method of least squares in determining the adjusted estimator. The proposed method is shown to be more and more efficient as the linear trend becomes stronger. It turns out to be relatively efficient as compared with the conventional methods if $\sigma$$^2$the variance of the random error term in the infinite superpopulation model, is not very large.

• Proceedings of the Korea Water Resources Association Conference
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• 2018.05a
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• pp.299-299
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• 2018

지역빈도해석은 수문관측자료의 보유기간이 짧은 지점 또는 미계측 지점에 대하여 보다 정확하며 신뢰할 수 있는 설계수문량을 산정하기 위해 널리 사용되고 있는 방법이다. 지역빈도해석에서 사용되는 가장 대표적인 모형인 홍수지수모형 (index flood model)은 각 지점의 표본평균을 홍수지수로 정의하고 이를 이용하여 설계수문량을 산정하는 방법이다. 모홍수지수모형 (population index flood model)은 표본평균을 홍수지수로 사용함으로써 발생하는 설계수문량의 왜곡과 오차를 극복하기 위해 제안된 방법으로 홍수지수를 미지의 모분포로 가정한 후 설계수문량을 산정한다. 본 연구에서는 모홍수지수모형을 국내 강우관측자료에 적용하여 지역빈도해석을 수행하고자 한다. 먼저, 이질성척도(heterogeneity)를 통해 지역동질성이 확인된 지역에 대하여 GEV 분포형을 적용한 비정상성 모홍수지수모형을 적용해 지역빈도해석을 수행하고 확률강우량을 산정하였다. 또한, 기존의 지점빈도해석 및 L-moment 기반의 지역빈도해석 결과와 비교를 통해 모홍수지수모형의 적용성을 확인하였다.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.25 no.1
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• pp.34-39
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• 2013

In this study, the quantitative analysis and pattern analysis of the error bounds with respect to recording period were carried out using the wave climate data from coastal areas. Arbitrary recording periods were randomly sampled from one month to six years using the bootstrap method. Based on the analysis, for recording periods less than one year, it was found that the error bounds decreased rapidly as the recording period increased. Meanwhile, the error bounds were found to decrease more slowly for recording periods longer than one year. Assuming the absolute estimate error to be around 10% (${\pm}0.1m$) for an one meter significant wave height condition, the minimum recording period for reaching the estimate error for Sokcho and Geoje-Hongdo stations satisfied this condition with over two years of data, while Anmado station was found to satisfy this condition when using observational data of over three years. The confidence intervals of the significant wave height clearly show an increasing pattern when the percentile value of the wave height increases. Whereas, the confidence intervals of the mean wave period are nearly constant, at around 0.5 seconds except for the tail regions, i.e., 2.5- and 97.5-percentile values. The error bounds for 97.5-percentile values of the wave height necessary for harbor tranquility analysis were found to be 0.75 m, 0.5 m, and 1.2 m in Sokcho, Geoje-Hongdo, and Anmado, respectively.

• The korean journal of orthodontics
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• v.37 no.1 s.120
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• pp.16-28
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• 2007

Objective: Evaluation of individual growth is important in orthodontics. The aim of this study was to develop a convenient software that can evaluate current growth status and predict further growth. Methods: Stature data of 2 to 20 year-old Koreans (4893 boys and 4987 girls) were extracted from a nationwide data. Age-sex-specific continuous functions describing percentile growth curves were constructed using natural cubic spline function (NCSF). Then, final stature prediction algorithm was developed and its validity was tested using longitudinal series of stature measurements on randomly selected 200 samples. Various accuracy measurements and analyses of errors between observed and predicted stature using NCSF growth curves were performed. Results: NCSF growth curves were shown to be excellent models in describing reference percentile stature growth curie over age. The prediction accuracy compared favorably with previous prediction models, even more accurate. The current prediction models gave more accurate results in girls than boys. Although the prediction accuracy was high, the error pattern of the validation data showed that in most cases, there were a lot of residuals with the same sign, suggestive of autocorrelation among them. Conclusion: More sophisticated growth prediction algorithm is warranted to enhance a more appropriate goodness of model fit for individual growth.