• 품질경영학회지
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• 제33권3호
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• pp.149-155
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• 2005

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2006년도 춘계학술대회
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• pp.135-141
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• 2006

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• Communications for Statistical Applications and Methods
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• 제13권1호
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• pp.39-47
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• 2006

The Bayesian approach to multiple testing procedure for one sample testing problem proposed by Scott and Berger (2003) is extended to two-sample comparison problem in microarray experiments. The prior distribution of each gene's mean for one sample is given conditionally on the corresponding gene's mean for the other sample. Posterior distributions of interesting parameters are derived and estimated based on an importance sampling method. A simulated example is given for illustration.

• 응용통계연구
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• 제18권1호
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• pp.197-210
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• 2005

본 연구에서는 중등학교 통계교육을 위하여, 제7차 수학과 교육과정 중 고등학교에서 사용하는 검정교과서 수학 1과 국정교과서 확률과 통계의 확률통계 영역을 중심으로 용어와 개념 및 표현을 비교, 연구하였다. 검정과 국정교과서의 표본표준편차의 정의가 일치되지 않았으며, 표분평균의 분산과 중심극한정리에 대한 개념설명이 교과서마다 상이하였다. 또한, 확률변수 개념 설명이 불분명 한 교과서도 발견되었다. 본 연구에서는 오류의 수정과 더불어 표본분산으로 불편추정량을 사용할 것을 제안하였다.

• Journal of the Korean Data and Information Science Society
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• 제28권2호
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• pp.443-449
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• 2017

Estimation of population proportion like the distribution rate of LED TV and the prevalence of a disease are often estimated based on survey sample data. Population proportion is generally considered as a special form of population mean. In complex sampling like stratified multistage sampling with unequal probability sampling, the denominator of mean may be random variable and it is estimated like ratio estimator. In this research, we examined the estimation of distribution rate based on stratified multistage sampling, and determined some numerical outcomes using stratified random sample data with about 25% of missing observations. In the data used for this research, the survey weight was determined by deterministic way. So, the weights are not random variable, and the population distribution rate and its variance estimator can be estimated like population mean estimation. When the weights are not random variable, if one estimates the variance of proportion estimator using ratio method, then the variances may be inflated. Therefore, in estimating variance for population proportion, we need to examine the structure of data and survey design before making any decision for estimation methods.

• Journal of the Korean Data and Information Science Society
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• 제11권1호
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• pp.57-64
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• 2000

By assuming a Type-I censored sample, we propose the approximate maximum likelihood estimators(AMLE) of the scale and location parameters of the gamma distribution. We compare the proposed estimators with the maximum likelihood estimators(MLE) in the sense of the mean squared errors(MSE) through Monte Carlo method.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1335-1344
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• 2008

The maximum likelihood method does not admit explicit solutions when the sample is multiply censored and progressive censored. So we shall propose some approximate maximum likelihood estimators (AMLEs) of the scale parameter for the power function distribution based on multiply Type-II censored samples and progressive Type-II censored samples when shape parameter is known. We compare the proposed estimators in the sense of the mean squared error (MSE) through Monte Carlo simulation for various censoring schemes.

• Communications for Statistical Applications and Methods
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• 제5권1호
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• pp.231-238
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• 1998

A two stage shrinkage testimator for the mean of an exponential distribution is considered with the assumption that an initial estimate of the mean is available. Mean squared error(MSE) of testimator and its relative efficiency (to usual single sample mean) are briefly reviewed. It is shown that relative efficiency depends only on the ratio of true mean value and its initial estimate.

• Journal of the Korean Data and Information Science Society
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• 제17권4호
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• pp.1319-1328
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• 2006

For multiply Type-II censored samples from two-parameter Rayleigh distribution, the maximum likelihood method does not admit explicit solutions. In this case, we propose some explicit estimators of the location and scale parameters in the Rayleigh distribution by the approximate maximum likelihood methods. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• 한국경영과학회지
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• 제31권1호
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• pp.15-24
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• 2006

In simulation input modeling, it is important to identify a probability distribution to represent the input process of interest. In this paper, an appropriate sample size is determined for parameter estimation associated with some typical probability distributions frequently encountered in simulation input modeling. For this purpose, a statistical measure is proposed to evaluate the effect of sample size on the precision as well as the accuracy related to the parameter estimation, square rooted mean square error to parameter ratio. Based on this evaluation measure, this sample size effect can be not only analyzed dimensionlessly against parameter's unit but also scaled regardless of parameter's magnitude. In the Monte Carlo simulation experiments, three continuous and one discrete probability distributions are investigated such as ; 1) exponential ; 2) gamma ; 3) normal ; and 4) poisson. The parameter's magnitudes tested are designed in order to represent distinct skewness respectively. Results show that ; 1) the evaluation measure drastically improves until the sample size approaches around 200 ; 2) up to the sample size about 400, the improvement continues but becomes ineffective ; and 3) plots of the evaluation measure have a similar plateau pattern beyond the sample size of 400. A case study with real datasets presents for verifying the experimental results.