• Journal of the Korean Statistical Society
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• 제27권4호
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• pp.459-469
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• 1998

Balanced half sample method is a simple variance estimation method for complex sampling designs. Since it is simple and flexible, it has been widely used in large scale sample surveys. However, the usual BHS method overestimate the true variance in without replacement sampling and two-stage cluster sampling. Focusing on this point , we proposed an unbiased BHS variance estimator in a stratified two-stage cluster sampling and then described an implementation method of the proposed estimator. Finally, partially BHS design is explained as a tool of reducing the number of replications of the proposed estimator.

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.563-568
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• 1995

It is well-known that the sample mean and the sample variance are jointly sufficient under normality assumption. In this paper a proof of the joint sufficiency is given without using the factorization criterion. It is related to a finite Sanov-type conditional theorem, i.e., the conditional probability density of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are independently and identically distributed (i.i.d.) normal random variables with mean m and variance $\delta^2$, equals that of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are i.i.d. normal random variables with mean $\mu$ and variance $\sigma^2$.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.131-142
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• 1999

Estimators for domains and approximate estimators of their variance are derived using post-stratified complex sample. Furthermore we propose an adjusted variance estimator of a domain mean in case of considering the post-stratified complex sample as simple random sample. A simulation study based on the data of Farm Household Economy Survey is presented to compare variance estimators numerically. From the study we showed that our adjusted variance estimator compensate for the under-estimation problem considerably.

• 응용통계연구
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• 제18권3호
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• pp.689-699
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• 2005

우리는 모분산 ${\sigma}^2$에 대한 추정량으로서 표본분산 $S^2=\frac{{\Sigma}^n_{i=1}(X_i-\={X})^2}{n-1}$을 주로 사용한다. 그러나, 제 7차 교육과정에 따른 고등학교 수학 교과서(10-가, 수학 I과 실용수학)에서는 표본분산의 정의를 $S^2_n=\frac{{\Sigma}^n_{i=1}(X_i-\={X})^2}{n}$로 사용하고 있다. 이 두 표본분산들의 관계를 알아보고, 시뮬레이션을 통하여 확인하여 본다. 또한, 이 두 표본분산들을 포함하여 일반적으로 정의할 수 있는 표본분산을 제안한다.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.249-259
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• 2002

In order to estimate the mean and variance for a Normal distribution which is truncated at both right and left sides, maximum likelihood estimators based on the entire sample from the original distribution are compared with the sample mean and variance of the censored sample which is the data remaining after truncation using simulation. We found that, surprisingly, the mean squared error of the mean based on the censored data Is smaller than that of the full sample estimators.

• Journal of the Korean Data and Information Science Society
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• 제28권5호
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• pp.981-999
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• 2017

단순확률모형을 고려하는 표준관리도에서는 표본간 분산을 고려하지 않고 공정분산을 추정한다. 표본간 분산이 존재하는 경우에는, 공정분산이 과소추정된다. 공정분산이 과소추정되면 좁아진 관리한계로 인해 관리도의 민감도는 향상되지만 과도한 오경보율을 발생시킨다. 이 논문에서는 공정모형으로 분산성분모형, 즉 변동의 원인을 표본내 분산과 표본간 분산으로 구분하는 확률모형을 고려한다. 관리한계는 표본내 분산과 표본간 분산을 모두 사용하여 설정하고 그에 따른 평균런길이를 통하여 효율을 살펴 보았다. 관리형태는 가장 널리 사용되는 ${\bar{X}}$, EWMA, CUSUM 관리도를 고려하였다. 관리한계 설정에서 표본내 분산만을 사용한 경우 (Case I)와 표본간 분산도 함께 사용한 경우 (Case II)를 통해 관리도의 효율을 비교하였다. 또한, 공정 모수가 주어진 경우와 추정된 두 경우에 대해서도 관리도의 효율을 비교하였다. 그 결과, 표본간 분산이 증가할 때 Case I의 오경보율은 급격히 증가한 반면 Case II의 경우에는 동일하게 유지됨을 알 수 있었다.

• 응용통계연구
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• 제21권1호
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• pp.177-182
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• 2008

공통분산을 갖는 두 모집단에서 얻은 두 독립표본 자료로부터 공통분산을 추정하거나, 한 모집단에서 얻는 두 자료의 혼합자료로부터 모분산을 추정할때 각 표본분산의 가중평균값인 합동추정량(pooled estimator)을 주로 사용한다. 본 논문에서는 동일한 모집단에서 얻은 혼합자료의 표본분산 식을 각 자료의 평균과 분산만 이용하여 구한 후 합동추정량과 비교한다.

• 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.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2023년도 학술발표회
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• pp.244-244
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• 2023

Both the frequency and the magnitude of hydrometeorological extreme events such as severe floods and droughts are increasing. In order to prevent a damage from the climatic disaster, hydrological models are often simulated under various meteorological conditions. While performing the simulations, a synthetic data generated through time series models which maintains the key statistical characteristics of the sample data are widely applied. However, the synthetic data can easily maintains both the average and the variance of the sample data, but the quantile is not maintained well. In this study, we proposes a data generation method which maintains the quantile of the sample data well. The equations of the former maintenance of variance extension (MOVE) are expanded to maintain quantile rather than the average or the variance of the sample data. The equations are derived and the coefficients are determined based on the characteristics of the sample data that we aim to preserve. Monte Carlo simulation is utilized to assess the performance of the proposed data generation method. A time series data (data length of 500) is regarded as the sample data and selected randomly from the sample data to create the data set (data length of 30) for simulation. Data length of the selected data set is expanded from 30 to 500 by using the proposed method. Then, the average, the variance, and the quantile difference between the sample data, and the expanded data are evaluated with relative root mean square error for each simulation. As a result of the simulation, each equation which is designed to maintain the characteristic of data performs well. Moreover, expanded data can preserve the quantile of sample data more precisely than that those expanded through the conventional time series model.